• 2015 Google Code Jam Round 1A (GCJ 15 Round 1A)
• 2015 Google Code Jam Round 1C (GCJ 15 Round 1C)
• 2015 Google Code Jam World Finals (GCJ 15 World Finals)
• 2016 Google Code Jam Round 1A (GCJ 16 Round 1A)
• 2016 Google Code Jam Round 1B (GCJ 16 Round 1B)
• 2016 Google Code Jam Round 1C (GCJ 16 Round 1C)
• 2016 Google Code Jam Round 2 (GCJ 16 Round 2)
• 2016 Google Code Jam Round 3 (GCJ 16 Round 3)
• 2016 Google Code Jam World Finals (GCJ 16 World Finals)
• 2017 Google Code Jam Round 1A (GCJ 17 Round 1A)
• 2017 Google Code Jam Qualification Round (GCJ 17 Qualification Round)
• 2017 Google Code Jam Round 1B (GCJ 17 Round 1B)
• 2017 Google Code Jam Round 1C (GCJ 17 Round 1C)
• 2017 Google Code Jam Round 2 (GCJ 17 Round 2)
• 2017 Google Code Jam Round 3 (GCJ 17 Round 3)
• 2017 Google Code Jam World Finals (GCJ 17 World Finals)
• 2018 Google Code Jam Round 1A (GCJ 18 Round 1A)
• 2018 Google Code Jam Round 1B (GCJ 18 Round 1B)
• 2018 Google Code Jam Round 2 (GCJ 18 Round 2)
• 2020 Google Code Jam Round 1A (GCJ 20 Round 1A)
• 2020 Google Code Jam Round 1C (GCJ 20 Round 1C)
• 2020 Google Code Jam Round 2 (GCJ 20 Round 2)
• 2020 Google Code Jam Virtual World Finals (GCJ 20 Virtual World Finals)
• 2019 Google Code Jam Qualification Round (GCJ 19 Qualification Round)

import sys
import requests
import json
import time
import random
import string
import hashlib

contestids = ['ids of gyms you used for testing']
participants = set()
key = open('key', 'r').read()
secret = open('secret', 'r').read()
for contestid in contestids:
    rand = ''.join([random.choice(string.ascii_letters + string.digits) for n in range(6)])
    params = [f'contestId={contestid}', 'showUnofficial=true', f'apiKey={key}', f'time={int(time.time())}']
    req_params = '&'.join(params)
    hash_params = '&'.join(sorted(params))
    h = hashlib.sha512(f'{rand}/contest.standings?{hash_params}#{secret}'.encode('utf-8'))
    sig = f'{rand}{h.hexdigest()}'
    req = f'https://mirror.codeforces.com/api/contest.standings?{req_params}&apiSig={sig}'
    standings = requests.get(req).json()['result']['rows']
    for row in standings:
        for participant in row['party']['members']:
            participants.add(participant['handle'])

participants = list(participants)
bounds    = [       3000,  2400,     2100,     1900,   1600,   1400,    1200,  -1000]
en_colors = ['red-black', 'red', 'yellow', 'purple', 'blue', 'cyan', 'green', 'grey']
rated_list = [[] for i in range(8)]
print(f'{len(participants)} testers:', *participants)
req = 'https://mirror.codeforces.com/api/user.info?handles='
for participant in participants:
    req += participant + ';'
resp = requests.get(req)
while resp.status_code != 200:
    time.sleep(1)
    resp = requests.get(req)
resp = resp.json()['result']
for participant in resp:
    for i in range(8):
        if bounds[i] <= participant['rating']:
            rated_list[i] += ['[user: ' + participant['handle'] + ']']
            break
sys.stdout = open('en.txt', 'w')
for i in range(8):
    if len(rated_list[i]) == 0:
        continue
    print(*rated_list[i], sep=', ', end=' ')
    print(f'for {en_colors[i]} testing')

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back



void solve() {
    int n,m,k,H; cin >> n >> m >> k >> H;
    int ans = 0;
    forn(i, n) {
        int x; cin >> x;
        ans += (H != x) && abs(H - x) % k == 0 && abs(H-x) <= (m-1) * k;
    }
    cout << ans << endl;
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include<bits/stdc++.h>
using namespace std;

bool solve(){
    int n;
    cin >> n;
    vector<int>a(n), b(n);
    for(int i = 0; i < n; i++){
        cin >> a[i];
        b[i] = a[i];
    }
    sort(b.begin(), b.end());
    for(int i = 0; i < n; i++){
        if((a[i] % 2) != (b[i] % 2)) return false;
    }
    return true;

}

int main(){
    int t;
    cin >> t;
    while(t--){
        cout << (solve() ? "YES" : "NO") << "\n";
    }
    return 0;
}

#include "bits/stdc++.h"
using namespace std;

bool solve(){
    int n, k;
    cin >> n >> k;
    vector<int>c(n);
    for(int i = 0; i < n; i++) cin >> c[i];
    int left = 0, right = 0, i = 0, j = n - 1;
    int k_left = k, k_right = k;

    if (c[0] == c[n - 1]){
        k_left = k / 2;
        k_right = k - k_left;
    }
    for(; i < n && left < k_left; i++){
        if(c[i] == c[0]) left++;
    }
    for(; j >= 0 && right < k_right; j--){
        if(c[j] == c[n - 1]) right++;
    }
    return (i - 1) < (j + 1);
}

int main(){
    int t;
    cin >> t;
    while(t--){
        cout << (solve() ? "YES" : "NO") << "\n";
    }

}

#include <iostream>
#include <vector>
#include <set>
#include <map>

using namespace std;

typedef long long ll;

ll n;

bool isPermutation(vector<ll> a) {
    for (int i = 0; i < n; ++i) {
        if (a[i] <= 0 || a[i] > n) {
            return false;
        }
    }
    set<ll> s(a.begin(), a.end());
    return s.size() == n;
}

vector<ll> prefSumToArray(vector<ll> p) {
    vector<ll> res(n);
    res[0] = p[0];
    for (int i = 1; i < n; ++i) {
        res[i] = p[i] - p[i - 1];
    }
    return res;
}

void solve() {
    cin >> n;
    vector<ll> a(n - 1);
    for (int i = 0; i + 1 < n; ++i) {
        cin >> a[i];
    }
    ll x = n * (n + 1) / 2;
    if (a.back() != x) {
        a.push_back(x);
        vector<ll> b = prefSumToArray(a);
        if (isPermutation(b)) {
            cout << "YES\n";
        } else {
            cout << "NO\n";
        }
        return;
    }
    map<ll, int> cnt;
    cnt[a[0]]++;
    for (int i = 1; i < n - 1; ++i) {
        cnt[a[i] - a[i - 1]]++;
    }
    vector<int> cntGt1;
    for (auto p: cnt) {
        if (p.second > 1) {
            cntGt1.push_back(p.first);
        }
    }
    if (cntGt1.size() > 1) {
        cout << "NO\n";
        return;
    }
    if (cntGt1.size() == 1) {
        int x1 = cntGt1[0];
        if (cnt[x1] > 2) {
            cout << "NO\n";
            return;
        }
    }
    vector<int> cnt0;
    for (int i = 1; i <= n; ++i) {
        if (cnt[i] == 0) {
            cnt0.push_back(i);
        }
    }
    if (cnt0.size() != 2) {
        cout << "NO\n";
        return;
    }
    cout << "YES\n";
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    int t;
    cin >> t;
    for (int _ = 0; _ < t; ++_) {
        solve();
    }
    return 0;
}

#include <bits/stdc++.h>

#define int long long

using namespace std;

vector<int> dp;
vector<bool> used;
vector<vector<int>> sl;

int get(int v){
    if(used[v]){
        return dp[v];
    }
    used[v] = true;
    int s = 0;
    for(int u: sl[v]){
        s += get(u);
    }
    if(!sl[v].empty()) dp[v] = min(dp[v], s);
    return dp[v];
}

void solve(int tc) {
    int n, k;
    cin >> n >> k;
    dp.resize(n);
    used.assign(n, false);
    sl.assign(n, vector<int>(0));
    for(int &e: dp) cin >> e;
    for(int i = 0; i < k; ++i){
        int e;
        cin >> e;
        dp[--e] = 0;
    }
    for(int i = 0; i < n; ++i){
        int m;
        cin >> m;
        sl[i].resize(m);
        for(int &e: sl[i]){
            cin >> e;
            --e;
        }
    }
    for(int i = 0; i < n; ++i){
        get(i);
    }
    for(int e: dp) cout << e << " ";
}

bool multi = true;

signed main() {
    int t = 1;
    if(multi) cin >> t;
    for (int i = 1; i <= t; ++i) {
        solve(i);
        cout << "\n";
    }
    return 0;
}

#include <bits/stdc++.h>
#define all(arr) arr.begin(), arr.end()

using namespace std;

const int MAXN = 200200;
const int MAXK = 30;
const int MAXMEM = MAXN * MAXK;

mt19937 rng(07062006);

struct node {
	node *chi[2] {nullptr};
	int sz = 0, id = -1;
};

int n, k;
int arr[MAXN];
node *mem = new node[MAXMEM];
node *root, *mpos;

void add_num(node* &v, int val, int i, int id) {
	if (v == nullptr) *(v = mpos++) = node();
	v->sz++;
	if (i == -1) {
		v->id = id;
		return;
	}
	add_num(v->chi[val >> i & 1], val, i - 1, id);
}

int down(node *v, int val, int i, int &x, int &jans) {
	if (i == -1) {
		jans = v->id;
		return 0;
	}
	int b = val >> i & 1;
	if (v->chi[b])
		return down(v->chi[b], val, i - 1, x ^= ((1 ^ b) << i), jans) | (1 << i);
	return down(v->chi[b ^ 1], val, i - 1, x ^= ((rng() & 1) << i), jans);
}

void build() {
	root = nullptr;
	mpos = mem;
	add_num(root, *arr, k - 1, 0);
}

tuple<int, int, int> solve() {
	int ians = 0, jans = 1, xans = 0;
	for (int i = 1; i < n; ++i) {
		int x = 0, j = -1;
		int cur = down(root, arr[i], k - 1, x, j);
		if (cur > ((arr[ians] ^ xans) & (arr[jans] ^ xans)))
			ians = j, jans = i, xans = x;
		add_num(root, arr[i], k - 1, i);
	}
	return {ians, jans, xans};
}

int main() {
	int t; cin >> t;
	while (t--) {
		cin >> n >> k;
		for (int i = 0; i < n; ++i)
			cin >> arr[i];
		build();
		auto [ians, jans, xans] = solve();
		cout << ++ians << ' ' << ++jans << ' ' << xans << endl;
	}
}

#include <bits/stdc++.h>

#define x first
#define y second
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

typedef long double ld;
typedef long long ll;

using namespace std;

struct dsu{
    vector<int> p, lvl;

    dsu(int n){
        p.resize(n);
        lvl.assign(n, 0);
        iota(all(p), 0);
    }

    int get(int i){
        if(i == p[i]) return i;
        return p[i] = get(p[i]);
    }

    bool unite(int a, int b){
        a = get(a);
        b = get(b);
        if(a == b){
            return false;
        }
        if(lvl[a] < lvl[b])swap(a, b);
        p[b] = a;
        if(lvl[a] == lvl[b]){
            ++lvl[a];
        }
        return true;
    }

    bool reachable(int a, int b){
        return get(a) == get(b);
    }
};

void solve(int tc) {
    int n, m;
    cin >> n >> m;
    vector<pair<int, int>> h(n);
    for(auto &e: h) cin >> e.x;
    for(int i = 0; i < n; ++i){
        h[i].y = i;
    }
    dsu graph(n);
    vector<vector<int>> sl(n);
    for(int i = 0; i < m; ++i){
        int u, v;
        cin >> u >> v;
        --u, --v;
        if(h[u].x > h[v].x) sl[u].emplace_back(v);
        else sl[v].emplace_back(u);
    }
    int q;
    cin >> q;
    vector<pair<pair<int, int>, pair<int, int>>> req(q);
    for(auto &e: req){
        cin >> e.y.x >> e.y.y >> e.x.x;
        --e.y.x, --e.y.y;
        e.x.x += h[e.y.x].x;
    }
    for(int i = 0; i < q; ++i){
        req[i].x.y = i;
    }

    sort(all(h));
    sort(all(req));
    vector<bool> ans(q);
    int j = 0;
    for(auto e: req){
        while (j < n && h[j].x <= e.x.x) {
            for(int u: sl[h[j].y]){
                graph.unite(h[j].y, u);
            }
            ++j;
        }
        ans[e.x.y] = graph.reachable(e.y.x, e.y.y);
    }
    for(bool e: ans) cout << (e? "YES": "NO") << "\n";
}

bool multi = true;

signed main() {
    int t = 1;
    if(multi) cin >> t;
    for (int i = 1; i <= t; ++i) {
        solve(i);
        if(i < t) cout << "\n";
    }
    return 0;
}

def solve():
    n = int(input())
    s = input()
    cnt = set()
    for i in range(1, n):
        cnt.add(s[i - 1] + s[i])
    print(len(cnt))


t = int(input())
for _ in range(t):
    solve()

#include<bits/stdc++.h>
using namespace std;
void  solve(){
    int n, k;
    cin >> n >> k;
    vector<pair<int, int>>a(n);
    vector<int>b(n), ans(n);
    for(int i = 0; i < n; i++){
        cin >> a[i].first;
        a[i].second = i;
    }
    for(auto &i : b) cin >> i;
    sort(b.begin(), b.end());
    sort(a.begin(), a.end());

    for(int i = 0; i < n; i++){
        ans[a[i].second] = b[i];
    }
    for(auto &i : ans) cout << i << ' ';
    cout << endl;
}
int main(){
    int t;
    cin >> t;
    while(t--) solve();
}

def solve():
    n = int(input())
    a = [int(x) for x in input().split()]
    a.sort()
    if a[0] % 2 == 1:
        print("YES")
        return
    for i in range(n):
        if a[i] % 2 == 1:
            print("NO")
            return
    print("YES")


t = int(input())
for _ in range(t):
    solve()

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back



void solve() {
    int n; cin >> n;
    vector<int> p(n);
    for (auto &e : p) cin >> e;

    int r = 0;
    for (int i = 0; i < n; ++i) {
        if (p[min(n-1, r+1)] <= p[min(n-1, i+1)]) {
            r = i;
        }
    }
    vector<int> ans;
    for (int i = r + 1; i < n; ++i) ans.eb(p[i]);
    ans.eb(p[r]);
    for (int i = r-1; i >= 0; --i) {
        if (p[i] > p[0]) {
            ans.eb(p[i]);
        } else {
            for (int j = 0; j <= i; ++j) {
                ans.eb(p[j]);
            }
            break;
        }
    }
    for (auto e : ans) cout << e << ' ';
    cout << endl;
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include <iostream>
#include <vector>
#include <set>
#include <queue>
#include <algorithm>

using namespace std;

typedef long long ll;

void solve() {
    int n;
    cin >> n;
    vector<int> a(n);
    vector<set<int>> g(n);
    vector<set<int>> neighbours(n);
    vector<int> d(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
        a[i]--;
        g[i].insert(a[i]);
        g[a[i]].insert(i);
    }
    for (int i = 0; i < n; ++i) {
        d[i] = g[i].size();
    }
    int bamboos = 0, cycles = 0;
    vector<bool> vis(n);
    for (int i = 0; i < n; ++i) {
        if (!vis[i]) {
            queue<int> q;
            q.push(i);
            vis[i] = true;
            vector<int> component = {i};
            while (!q.empty()) {
                int u = q.front();
                q.pop();
                for (int v: g[u]) {
                    if (!vis[v]) {
                        vis[v] = true;
                        q.push(v);
                        component.push_back(v);
                    }
                }
            }
            bool bamboo = false;
            for (int j: component) {
                if (d[j] == 1) {
                    bamboo = true;
                    break;
                }
            }
            if (bamboo) {
                bamboos++;
            } else {
                cycles++;
            }
        }
    }
    cout << cycles + min(bamboos, 1) << ' ' << cycles + bamboos << '\n';
}

int main() {
    int t;
    cin >> t;
    for (int _ = 0; _ < t; ++_) {
        solve();
    }
}

/*
         `)
        _ \
      (( }/  ,_
      )))__ /
     (((---'
       \ '
        )|____.---- )
       / \ `       (
      / ' \ `      )
     /  '  \  `   /
    /   '       _/
   /   _!____.-'
  /_.-'/    \
     |`_    |`_
*/
#include <bits/stdc++.h>

using namespace std;
typedef pair<int, int> ipair;

const int MAXN = 200200;
const int MAXK = MAXN;
const int MOD = 1000000007;

inline int add(int a, int b) {
	return (a + b >= MOD ? a + b - MOD : a + b);
}

inline int mul(int a, int b) {
	return 1LL * a * b % MOD;
}

int n, m, k;
int arr[MAXN], brr[MAXN], cnt[MAXK];

void build() {
	sort(arr, arr + n);
	memcpy(brr, arr, sizeof(int) * n);
	k = unique(arr, arr + n) - arr;
	for (int j = 0; j < k; ++j)
		cnt[j] = upper_bound(brr, brr + n, arr[j]) - lower_bound(brr, brr + n, arr[j]);
}

inline void push(stack<ipair> &S, int x) {
	S.emplace(x, mul(x, S.empty() ? 1 : S.top().second));
}

int solve() {
	if (k < m) return 0;
	stack<ipair> S1, S2;
	for (int j = 0; j < m; ++j)
		push(S1, cnt[j]);
	int ans = 0;
	for (int j = m; j <= k; ++j) {
		if (arr[j - 1] - arr[j - m] == m - 1)
			ans = add(ans, mul(S1.empty() ? 1 : S1.top().second, S2.empty() ? 1 : S2.top().second));
		if (S2.empty()) {
			for (; !S1.empty(); S1.pop())
				push(S2, S1.top().first);
		}
		S2.pop();
		push(S1, cnt[j]);
	}
	return ans;
}

int main() {
	int t; cin >> t;
	while (t--) {
		cin >> n >> m;
		for (int i = 0; i < n; ++i)
			cin >> arr[i];
		build();
		cout << solve() << endl;
	}
}

#include <bits/stdc++.h>

using namespace std;
typedef pair<int, int> ipair;

const int MAXN = 200200;

int n;
vector<ipair> gr[MAXN];
vector<int> res;
queue<int> qu;
int par[MAXN], ipar[MAXN], deg[MAXN], hard[MAXN];

void init() {
	res.clear();
	while (!qu.empty()) qu.pop();
	memset(deg, 0, sizeof(int) * n);
	memset(hard, 0, sizeof(int) * n);
	for (int v = 0; v < n; ++v)
		gr[v].clear();
}

void dfs(int v, int p, int ip) {
	par[v] = p;
	ipar[v] = ip;
	for (auto [u, i]: gr[v]) {
		if (u == p) continue;
		dfs(u, v, i);
		++deg[v];
		hard[v] += (deg[u] > 0);
	}
}

void build() {
	dfs(0, -1, -1);
}

bool rempar(int v) {
	int u = par[v];
	if (u == -1) return true;
	par[v] = -1;
	res.push_back(ipar[v]);
	--deg[u], --hard[u];
	if (deg[u]) {
		if (!hard[u]) qu.push(u);
		return true;
	}
	if (par[u] == -1) return false;
	--hard[par[u]];
	if (!hard[par[u]]) qu.push(par[u]);
	return true;
}

bool solve() {
	if (n % 3) return false;
	for (int v = 0; v < n; ++v)
		if (!hard[v] && deg[v]) qu.push(v);
	while (!qu.empty()) {
		int v = qu.front(); qu.pop();
		if (deg[v] > 2) return false;
		if (deg[v] == 2) {
			if (!rempar(v)) return false;
		} else if (deg[v] == 1) {
			if (par[v] == -1) return false;
			for (auto [u, i]: gr[par[v]]) {
				if (u == par[par[v]] || u == v || par[u] == -1) continue;
				if (!deg[u]) return false;
				res.push_back(i);
				par[u] = -1;
			}
			if (!rempar(par[v])) return false;
		}
	}
	return true;
}

int main() {
	int t; cin >> t;
	while (t--) {
		cin >> n, init();
		for (int i = 1; i < n; ++i) {
			int v, u; cin >> v >> u, --v, --u;
			gr[v].emplace_back(u, i);
			gr[u].emplace_back(v, i);
		}
		build();
		if (!solve()) {
			cout << -1 << endl;
			continue;
		}
		cout << res.size() << endl;
		for (int id: res)
			cout << id << ' ';
		cout << endl;
	}
}

#include <iostream>

using namespace std;

void solve() {
    int n, d;
    cin >> n >> d;
    string s;
    cin >> s;
    for (int i = 0; i < n; ++i) {
        if (s[i] - '0' >= d) {
            cout << s[i];
        } else {
            cout << d;
            for (int j = i; j < n; ++j) {
                cout << s[j];
            }
            cout << '\n';
            return;
        }
    }
    cout << d << '\n';
}

int main() {
    int t;
    cin >> t;
    for (int _ = 0; _ < t; ++_) {
        solve();
    }
    return 0;
}

def layer(n, x, y):
    return min([x, y, n + 1 - x, n + 1 - y])


def solve():
    n, x1, y1, x2, y2 = map(int, input().split())
    print(abs(layer(n, x1, y1) - layer(n, x2, y2)))


t = int(input())
for _ in range(t):
    solve()

#include "bits/stdc++.h"
using namespace std;

void solve(){
    int n;
    cin >> n;
    vector<int>b(n-1), a;
    for(int i = 0; i < n - 1; i++) cin >> b[i];
    a.emplace_back(b[0]);
    for(int i = 0; i < n - 2; i++){
        a.emplace_back(min(b[i], b[i + 1]));
    }
    a.emplace_back(b[n - 2]);
    for(auto &i : a) cout << i << ' ';
    cout << "\n";
}
int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 50;

int fib[MAXN];

void build() {
	fib[0] = fib[1] = 1;
	for (int i = 2; i < MAXN; ++i)
		fib[i] = fib[i - 2] + fib[i - 1];
}

bool solve(int n, int x, int y) {
	if (n == 1) return true;
	if (fib[n - 1] <= y && y < fib[n])
		return false;
	if (fib[n] <= y)
		y -= fib[n];
	return solve(n - 1, y, x);
}

int main() {
	int t; cin >> t;
	build();
	while (t--) {
		int n, x, y; cin >> n >> x >> y;
		cout << (solve(n, --x, --y) ? "YES" : "NO") << '\n';
	}
}

#include <iostream>
#include <cmath>
#include <cctype>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
#include <deque>
#include <stack>
#include <unordered_set>
#include <sstream>
#include <cstring>
#include <iomanip>
#include <queue>
#include <unordered_map>
#include <random>
#include <cfloat>
#include <chrono>
#include <bitset>
#include <complex>
#include <immintrin.h>

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);

    int32_t num_tests;
    std::cin >> num_tests;

    for(int32_t t = 0; t < num_tests; t++) {
        int64_t k;
        std::cin >> k;

        std::vector<int32_t> digits;
        while(k > 0) {
            digits.push_back(k % 9);
            k /= 9;
        }
        std::reverse(digits.begin(), digits.end());

        for(int32_t i = 0; i < digits.size(); i++)
            std::cout << (char)(digits[i] < 4 ? (digits[i] + '0') : (digits[i] + '1'));
        std::cout << "\n";
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

int sz(int v, vector<vector<int>> &g, vector<bool> &used){
    used[v] = true;
    int s = 1;
    for(int u: g[v]){
        if(!used[u]) s += sz(u, g, used);
    }
    return s;
}

void remove(vector<int> &from, int x){
    for(int &e: from){
        if(e == x){
            swap(e, from.back());
            from.pop_back();
            return;
        }
    }
}

void solve(int tc) {
    int n, m;
    cin >> n >> m;
    vector<vector<int>> sl(n);
    for(int i = 0; i < m; ++i){
        int u, v;
        cin >> u >> v;
        sl[--u].emplace_back(--v);
        sl[v].emplace_back(u);
    }
    int k = sqrt(n);
    if(n != k * k || m != n + k){
        cout << "NO";
        return;
    }
    for(int i = 0; i < n; ++i){
        if(sl[i].size() != 2 && sl[i].size() != 4){
            cout << "NO";
            return;
        }
    }
    vector<bool> used(n);
    if(sz(0, sl, used) != n){
        cout << "NO";
        return;
    }
    for(int i = 0; i < n; ++i){
        if(sl[i].size() == 2) continue;
        for(int j = 0; j < sl[i].size();){
            int u = sl[i][j];
            if(sl[u].size() > 2){
                remove(sl[i], u);
                remove(sl[u], i);
            }
            else{
                j++;
            }
        }
    }
    used = vector<bool>(n);
    for(int i = 0; i < n; ++i){
        if(!used[i] && sz(i, sl, used) != k){
            cout << "NO";
            return;
        }
    }
    cout << "YES";
}

bool multi = true;

signed main() {
    cout.tie(nullptr);
    int t = 1;
    if (multi)cin >> t;
    for (int i = 1; i <= t; ++i) {
        solve(i);
        cout << "\n";
    }
    return 0;
}

M = 10 ** 9 + 7


def pw(a, n):
    if n == 0:
        return 1
    b = pw(a, n // 2)
    return b * b % M * (a if n % 2 == 1 else 1) % M


def obr(x):
    return pw(x, M - 2)


def cnk(n, k):
    return fact[n] * obr(fact[k]) % M * obr(fact[n - k]) % M


def solve():
    n, k = map(int, input().split())
    c = [-1] + [int(x) for x in input().split()]
    if k == 1:
        print(1)
        return
    dp = [[0] * (n // k + 1) for i in range(n + 1)]  # dp[i][j] = number for i prefix with j blocks
    dp[0][0] = 1
    for i in range(1, n + 1):
        for j in range(0, n // k + 1):
            if j > 0:
                sz = 1
                for s in range(i - 1, - 1, -1):
                    if c[s] == c[i]:
                        sz += 1
                        if sz >= k:
                            dp[i][j] += dp[s - 1][j - 1] * cnk(sz - 2, k - 2) % M
                            dp[i][j] %= M
            dp[i][j] += dp[i - 1][j]
            dp[i][j] %= M
    for j in range(n // k, -1, -1):
        if dp[n][j] > 0:
            print(dp[n][j])
            return


t = int(input())
fact = [1] * 101
for i in range(1, 101):
    fact[i] = fact[i - 1] * i % M
for _ in range(t):
    solve()

from sys import stdin
input = lambda: stdin.readline().strip()


M = 10 ** 9 + 7
cnk = [[0] * (5000 + 1) for i in range(5000 + 1)]


def solve():
    n, k = map(int, input().split())
    c = [-1] + [int(x) for x in input().split()]
    if k == 1:
        print(1)
        return
    dp = [[0, 0] for i in range(n + 1)]  # dp[i] = [number, max] for i prefix
    dp[0][0] = 1
    for i in range(1, n + 1):
        sz = 1
        for s in range(i - 1, - 1, -1):
            if c[s] == c[i]:
                sz += 1
                if sz == k:
                    dp[i][1] = dp[s - 1][1] + 1
                if sz >= k:
                    if dp[s - 1][1] < dp[i][1] - 1:
                        break
                    dp[i][0] += dp[s - 1][0] * cnk[sz - 2][k - 2] % M
                    dp[i][0] %= M
        if dp[i][1] < dp[i - 1][1]:
            dp[i] = [0, dp[i - 1][1]]
        if dp[i][1] == dp[i - 1][1]:
            dp[i][0] += dp[i - 1][0]
            dp[i][0] %= M
    print(dp[n][0])


for i in range(5000 + 1):
    cnk[i][0] = 1
for i in range(1, 5000 + 1):
    for j in range(1, i + 1):
        cnk[i][j] = (cnk[i - 1][j] + cnk[i - 1][j - 1]) % M

t = int(input())
for _ in range(t):
    solve()

#include <bits/stdc++.h>
using namespace std;

void solve(){
    int n;
    cin >> n;
    string s;
    cin >> s;
    transform(s.begin(), s.end(), s.begin(), [] (char c) {
        return tolower(c);
    });
    s.erase(unique(s.begin(), s.end()), s.end());
    cout << (s == "meow" ? "YES" : "NO") << "\n";
}

int main(){
    int t;
    cin >> t;
    while(t--) solve();
}

#include <bits/stdc++.h>
using namespace std;
const int N = 26;

void solve(){
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    vector<int>big(N, 0), small(N, 0);
    for(auto &i : s){
        if('A' <= i && 'Z' >= i) big[i - 'A']++;
        else small[i - 'a']++;
    }
    int answer = 0;
    for(int i = 0; i < N; i++){
        int pairs = min(small[i], big[i]);
        answer += pairs;
        small[i] -=pairs; big[i] -= pairs;
        int add = min(k, max(small[i], big[i]) / 2);
        k -= add; answer += add;
    }
    cout << answer << endl;
}
int main(){
    int t;
    cin >> t;
    while(t--) solve();
    return 0;
}

def solve():
    n = int(input())
    s = [int(x) for x in input().split()]
    ans = 0
    buffs = [0] * n
    for e in s:
        if e > 0:
            buffs += [e]
            j = len(buffs) - 1
            while buffs[j] < buffs[j - 1]:
                buffs[j], buffs[j - 1] = buffs[j - 1], buffs[j]
                j -= 1
        else:
            ans += buffs.pop()
    print(ans)


t = int(input())
for _ in range(t):
    solve()

from queue import PriorityQueue


def solve():
    n = int(input())
    s = [int(x) for x in input().split()]
    ans = 0
    buffs = PriorityQueue()
    for e in s:
        if e > 0:
            buffs.put(-e)
        elif not buffs.empty():
            ans -= buffs.get()
    print(ans)


t = int(input())
for _ in range(t):
    solve()

#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <set>

using namespace std;

void solve() {
    int n;
    cin >> n;
    string s;
    cin >> s;
    int res = n - 1;
    for (int i = 1; i + 1 < n; ++i) {
        if (s[i - 1] == s[i + 1]) {
            res--;
        }
    }
    cout << res << '\n';
}

int main(int argc, char* argv[]) {
    int t;
    cin >> t;
    for (int i = 0; i < t; ++i) {
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back


void slow_solve(int n, int k, string s, string t) {
    set<string> was;

    queue<string> q;
    q.push(s);
    was.insert(s);

    auto add = [&](string& s, int i, int j) {
        if (i >= 0 && i < j && j < n) {
            swap(s[i], s[j]);
            if (!was.count(s)) {
                was.insert(s);
                q.push(s);
            }
            swap(s[i], s[j]);
        }

    };

    while (!q.empty()) {
        s = q.front(); q.pop();
        for (int i = 0; i < n; ++i) {
            add(s, i, i+k);
            add(s, i, i+k+1);
            add(s, i-k, i);
            add(s, i-k-1, i);
        }
    }
    cout << (was.count(t) ? "Yes" : "No") << '\n';
}

void solve() {
    int n,k; cin >> n >> k;
    string s; cin >> s;
    string t; cin >> t;

    if (n <= 5) {
        slow_solve(n, k, s, t);
        return;
    }
    map<char, int> cnt;
    for (char c : s) {
        cnt[c]++;
    }

    for (char c : t) {
        cnt[c]--;
    }

    bool ok = true;
    for (auto [c, x] : cnt) {
        ok &= x == 0;
    }
    cout << (ok ? "Yes" : "No") << '\n';
}

int main() {
    int t;
    cin >> t;

    while (t--) {
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back

void solve() {
    int n, k; cin >> n >> k;
    string s; cin >> s;
    string t; cin >> t;
    vector<int> cnt(26, 0);

    bool ok = true;
    for (int i = 0; i < n; ++i) {
        if (i >= k || i+k < n){
            cnt[s[i] - 'a']++;
            cnt[t[i] - 'a']--;
        } else {
            ok &= s[i] == t[i];
        }
    }

    cout << (ok && count(all(cnt), 0) == 26 ? "YES" : "NO") << '\n';
}

int main() {
    int t;
    cin >> t;

    while (t--) {
        solve();
    }
}

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2,avx,fma,bmi2")

#include <bits/stdc++.h>
#include <immintrin.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;

#define endl '\n'
//#define int long long
#define all(arr) arr.begin(), arr.end()
#define multitest() int _gorilla_silverback; cin >> _gorilla_silverback; while (_gorilla_silverback --> 0)
#define pikachu push_back
#define ls(id) (id << 1 | 1)
#define rs(id) ((id << 1) + 2)
#define sqr(x) ((x) * (x))
#define dlg(x) (31 - __builtin_clz(x))
#define ulg(x) (32 - __builtin_clz(x))

typedef pair<int, int> ipair;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> treap;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int MAXN = 200200;
const int L = 26;

int n;
string srr[MAXN];
int arr[MAXN], brr[MAXN], crr[MAXN];

void build() {
	for (int i = 0; i < n; ++i) {
		for (char c: srr[i]) {
			arr[i] ^= (1 << (c - 'a'));
			brr[i] |= (1 << (c - 'a'));
		}
	}
}

long long calc(int c) {
	int k = 0;
	for (int i = 0; i < n; ++i)
		if (brr[i] >> c & 1 ^ 1) crr[k++] = arr[i];
	sort(crr, crr + k);
	int mask = -1 & ((1 << L) - 1) ^ (1 << c);
	long long ans = 0;
	for (int i = 0; i < k; ++i) {
		auto itl = lower_bound(crr, crr + k, crr[i] ^ mask);
		auto itr = upper_bound(crr, crr + k, crr[i] ^ mask);
		ans += itr - itl;
	}
	return ans >> 1LL;
}

long long solve() {
	long long ans = 0;
	for (int c = 0; c < L; ++c)
		ans += calc(c);
	return ans;
}

signed main() {
	ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
	cin >> n;
	for (int i = 0; i < n; ++i)
		cin >> srr[i];
	build();
	cout << solve() << endl;
}

#include <bits/stdc++.h>

#define int long long
#define pb emplace_back
#define mp make_pair
#define x first
#define y second
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

typedef long double ld;
typedef long long ll;

using namespace std;

mt19937 rnd(time(nullptr));

const int inf = 2e18;
const ll M = 1e9;
const ld pi = atan2(0, -1);
const ld eps = 1e-6;

int last;
map<vector<int>, int> eq;
map<int, bool> symmetrical;

int dfs(int v, int p, vector<vector<int>> &sl){
    vector<int> children;
    for(int u: sl[v]){
        if(u == p) continue;
        children.emplace_back(dfs(u, v, sl));
    }
    sort(all(children));
    if(!eq.count(children)){
        map<int, int> cnt;
        for(int e: children){
            cnt[e]++;
        }
        int odd = 0, bad = 0;
        for(auto e: cnt){
            if(e.y & 1){
                odd++;
                bad += !symmetrical[e.x];
            }
        }
        eq[children] = last;
        symmetrical[last] = odd < 2 && bad == 0;
        last++;
    }
    return eq[children];
}

void solve(int tc){
    int n;
    cin >> n;
    eq.clear();
    symmetrical.clear();
    eq[vector<int>(0)] = 0;
    symmetrical[0] = true;
    last = 1;
    vector<vector<int>> sl(n);
    for(int i = 1; i < n; ++i){
        int u, v;
        cin >> u >> v;
        sl[--u].emplace_back(--v);
        sl[v].emplace_back(u);
    }
    cout << (symmetrical[dfs(0, 0, sl)]? "YES" : "NO");
}

bool multi = true;

signed main() {
    int t = 1;
    if (multi)cin >> t;
    for (int i = 1; i <= t; ++i) {
        solve(i);
        cout << "\n";
    }
    return 0;
}

t = int(input())
pi = '31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679'
for _ in range(t):
    n = input() + '#'
    for i in range(len(n)):
        if pi[i] != n[i]:
            print(i)
            break

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 55;

int n, s1, s2;
vector<int> res;

void solve() {
	res.clear();
	int d = s1 - s2;
	for (; s2 >= d; s2 -= d)
		res.push_back(d);
	if (s2) res.push_back(s2);
	for (int i = 0; i < res.size() && res.size() + 1 < n;) {
		if (res[i] == 1) {
		    ++i;
		    continue;
		}
		--res[i];
		res.push_back(1);
	}
	res.push_back(d);
}

int main() {
	int t; cin >> t;
	while (t--) {
		cin >> n >> s1 >> s2;
		solve();
		sort(res.begin(), res.end());
		for (int x: res)
			cout << x << ' ';
		cout << endl;
	}
}

#include "bits/stdc++.h"
using namespace std;
int n;

void solve(){
    cin >> n;
    vector<vector<int>>perm(n, vector<int>(n - 1));
    vector<int>p(n, 0);
    vector<int>cnt(n + 1, 0);
    for(int i = 0; i < n; i++){
        p[i] = i + 1;
        for(int j = 0; j < n - 1; j++){
            cin >> perm[i][j];
            if(j == 0) cnt[perm[i][j]]++;
        }
    }
    for(int i = 1; i <= n; i++){
        if(cnt[i] == n - 1){
            p[0] = i;
            break;
        }
    }
    for(int i = 0; i < n; i++){
        if(perm[i][0] != p[0]){
            for(int j = 0; j < n - 1; j++){
                p[j + 1] = perm[i][j];
            }
        }
    }
    for(int i = 0; i < n; i++) cout << p[i] << ' ';
    cout << endl;

}

int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
    return 0;
}

#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <set>

using namespace std;

void solve() {
    int n;
    cin >> n;
    vector<int> a(n);
    map<int, int> cnt;
    set<int> b;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
        cnt[a[i]]++;
        b.insert(a[i]);
        b.insert(a[i] + 1);
    }
    int last = 0;
    int res = 0;
    for (auto x: b) {
        int c = cnt[x];
        res += max(0, c - last);
        last = c;
    }
    cout << res << '\n';
}

int main(int argc, char* argv[]) {
    int t;
    cin >> t;
    for (int i = 0; i < t; ++i) {
        solve();
    }
}

t = int(input())
for _ in range(t):
    x = int(input())
    a = x
    b = 0
    for i in range(32, -1, -1):
        if x & (1 << i) > 0:
            continue
        if 2 * x - a - b >= (2 << i):
            a += 1 << i
            b += 1 << i
    if a + b == 2 * x and a ^ b == x:
        print(a, b)
    else:
        print(-1)

#include <bits/stdc++.h>
using namespace std;

const int MAXN = 200200;
const int INF = 1e9;

int n, ANS = INF;
int crr[MAXN], dist[MAXN], res[MAXN];
bool clr[MAXN];
vector<int> gr[MAXN];

void init() {
	ANS = INF;
	for (int v = 0; v < n; ++v)
		gr[v].clear();
	fill(dist, dist + n, INF);
	memset(clr, 0, n);
}

void dfs(int v, int p) {
	if (dist[v] >= ANS) return;
	if (clr[v]) ANS = min(ANS, dist[v]);
	for (int u: gr[v]) {
		if (u == p) continue;
		if (dist[v] + 1 < dist[u]) {
			dist[u] = dist[v] + 1;
			dfs(u, v);
		} else ANS = min(ANS, dist[v] + 1 + dist[u]);
	}
}

void solve() {
	dist[*crr] = 0;
	dfs(*crr, -1);
	clr[*crr] = true;
	for (int i = 1; i < n; ++i) {
		dist[crr[i]] = 0;
		dfs(crr[i], -1);
		clr[crr[i]] = true;
		res[i] = ANS;
	}
}

int main() {
	int gorilla; cin >> gorilla;
	while (gorilla--) {
		cin >> n >> *crr, --(*crr);
		init();
		for (int i = 1; i < n; ++i)
			cin >> crr[i], --crr[i];
		for (int i = 1; i < n; ++i) {
			int v, u; cin >> v >> u, --v, --u;
			gr[v].push_back(u);
			gr[u].push_back(v);
		}
		solve();
		for (int i = 1; i < n; ++i)
			cout << res[i] << ' ';
		cout << '\n';
	}
}

#include<bits/stdc++.h>

using namespace std;

void solve()
{
    int n;
    cin >> n;
    vector<int> token(n), boni(n);
    vector<vector<int>> g(n);
    vector<int> good(n);
    int m;
    cin >> m;
    int p, b;
    cin >> p >> b;
    for(int i = 0; i < p; i++)
    {
        int x;
        cin >> x;
        --x;
        token[x] = 1;
    }
    for(int i = 0; i < b; i++)
    {
        int x;
        cin >> x;
        --x;
        boni[x] = 1;
    }
    for(int i = 0; i < m; i++)
    {
        int x, y;
        cin >> x >> y;
        --x;
        --y;
        g[x].push_back(y);
        g[y].push_back(x);
    }
    for(int i = 0; i < n; i++)
        for(auto x : g[i])
            if(boni[i] && boni[x]) good[i] = 1;
    set<int> good_tokens;
    set<int> not_so_good_tokens;
    for(int i = 0; i < n; i++)
        for(auto x : g[i])
        {
            if(token[i] && good[x]) good_tokens.insert(i);
            else if(token[i] && boni[x]) not_so_good_tokens.insert(i);
        }
    vector<int> d(n, int(1e9));
    queue<int> q;
    d[0] = 0;
    q.push(0);
    while(!q.empty())
    {
        int k = q.front();
        q.pop();
        for(auto x : g[k])
        {
            if(d[x] > d[k] + 1)
            {
                d[x] = d[k] + 1;
                if(boni[x]) q.push(x);
            }
        }
    }
    bool has_ans = false;
    for(int i = 0; i < n; i++)
    {
        if(!token[i] || d[i] > n) continue;
        has_ans |= (!good_tokens.empty() && (*good_tokens.begin() != i || *good_tokens.rbegin() != i));
        int cnt = not_so_good_tokens.size();
        if(not_so_good_tokens.count(i)) cnt--;
        has_ans |= d[i] <= 1 + cnt;
    }
    cout << (has_ans ? "YES" : "NO") << endl;
}

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
#ifdef _DEBUG
    freopen("input.txt", "r", stdin);
#endif
    int tc = 1;
    cin >> tc;
    for(int i = 0; i < tc; i++)
    {
        solve();
    }
}

full = 'Yes' * 18
t = int(input())
for _ in range(t):
    if full.find(input()) >= 0:
        print('YES')
    else:
        print('NO')

t = int(input())
for _ in range(t):
    n, s = map(int, input().split())
    a = [int(x) for x in input().split()]
    s += sum(a)
    sm = 0
    cnt = 0
    for i in range(1, s + 1):
        if sm >= s:
            break
        sm += i
        cnt = i
    if sm != s or max(a) > cnt or cnt <= n:
        print("NO");
    else:
        print("YES")

def solve():
    l, r, x = map(int, input().split())
    a, b = map(int, input().split())
    if a == b:
        return 0
    if abs(a - b) >= x:
        return 1
    if r - max(a, b) >= x or min(a, b) - l >= x:
        return 2
    if r - b >= x and a - l >= x or r - a >= x and b - l >= x:
        return 3
    return -1


t = int(input())
for _ in range(t):
    print(solve())

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back

using ll = long long;

void solve() {
    ll n,m; cin >> n >> m;
    ll n0 = n;
    int cnt2 = 0, cnt5 = 0;
    ll k = 1;
    while (n > 0 && n % 2 == 0) {
        n /= 2;
        cnt2++;
    }
    while (n > 0 && n % 5 == 0) {
        n /= 5;
        cnt5++;
    }
    while (cnt2 < cnt5 && k * 2 <= m) {
        cnt2++;
        k *= 2;
    }
    while (cnt5 < cnt2 && k * 5 <= m) {
        cnt5++;
        k *= 5;
    }
    while (k * 10 <= m) {
        k *= 10;
    }
    if (k == 1) {
        cout << n0 * m << endl;
    } else {
        k *= m / k; // 1 <= m/k < 10
        cout << n0 * k << endl;
    }
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 200200;

int n;
int arr[MAXN];

int solve(int i, long long h, int s2, int s3) {
	if (i == n) return 0;
	if (arr[i] < h)
		return solve(i + 1, h + (arr[i] / 2), s2, s3) + 1;
	int ans1 = (s2 ? solve(i, h * 2, s2 - 1, s3) : 0);
	int ans2 = (s3 ? solve(i, h * 3, s2, s3 - 1) : 0);
	return max(ans1, ans2);
}

int main() {
	int t; cin >> t;
	while(t--) {
		long long h; cin >> n >> h;
		for (int i = 0; i < n; ++i)
			cin >> arr[i];
		sort(arr, arr + n);
		cout << solve(0, h, 2, 1) << endl;
	}
}

#pragma GCC optimize("Ofast")

#include <bits/stdc++.h>

using namespace std;

#include <ext/pb_ds/assoc_container.hpp>

using namespace __gnu_pbds;

typedef long long ll;
typedef long double ld;
typedef tree<pair<int, int>, null_type, less<>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

int newDigit = -1;

bool check(set<int> digits, int l, int r, bool useNewDigit) {
    for (int i = l; i <= r; ++i) {
        if (useNewDigit && i == newDigit) {
            continue;
        }
        if (!digits.count(i)) {
            return false;
        }
    }
    return true;
}

void solve() {
    int n, p;
    cin >> n >> p;
    vector<int> a(n + 1);
    set<int> digits;
    for (int i = 1; i <= n; ++i) {
        cin >> a[i];
        digits.insert(a[i]);
    }
    if (digits.size() == p) {
        cout << "0\n";
        return;
    }
    for (int i = n - 1; i >= 0; --i) {
        if (a[i] < p - 1) {
            newDigit = a[i] + 1;
            break;
        }
    }
    int l = 0, r = p - 1;
    int x = a[n];
    while (l < r) {
        int m = (l + r) >> 1;
        bool res = false;
        if (x + m >= p) {
            if (check(digits, x + m + 1 - p, x - 1, true)) {
                res = true;
            }
        } else {
            if (check(digits, 0, x - 1, false) && check(digits, x + m + 1, p - 1, false)) {
                res = true;
            }
        }
        if (res) {
            r = m;
        } else {
            l = m + 1;
        }
    }
    cout << l << '\n';
}

bool multitest = true;

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    cout.precision(25);
    size_t number_of_tests = 1;
    if (multitest) {
        cin >> number_of_tests;
    }
    for (size_t _ = 0; _ < number_of_tests; ++_) {
        solve();
    }
    return 0;
}

#include "bits/stdc++.h"
using namespace std;
int n;

void solve(){
    cin >> n;
    vector<int>b(n / 2), p(n);
    vector<bool>isUsed(n + 1, false);
    set<int>unused;

    for(int i = 0; i < n / 2; i++){
        cin >> b[i];
        p[i * 2 + 1] = b[i];
        isUsed[b[i]] = true;
    }
    for(int i = 1; i <= n; i++){
        if(!isUsed[i]) unused.insert(i);
    }


    if(int(unused.size()) != n / 2){
        cout << "-1\n";
        return;
    }

    for(int i = n / 2 - 1; i >= 0; i--){
        auto k = unused.upper_bound(p[2 * i + 1]);
        if(k == unused.begin()){
            cout << "-1\n";
            return;
        }

        k--;


        if(*k < p[2 * i + 1]){
            p[2 * i] = *k;
            unused.erase(k);
        }
        else{
            cout << "-1\n";
            return;
        }
    }
    for(auto i : p) cout << i << ' ';
    cout << endl;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int t;
    cin >> t;
    while(t--){
        solve();
    }

}

#include <bits/stdc++.h>
 
using namespace std;
 
#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back
 
 
void ct(char c) {
    cout << c << '\n';
}
 
void solve() {
    string a,b; cin >> a >> b;
    char ca = a.back();
    char cb = b.back();
    if (ca == cb) {
        if (sz(a) == sz(b)) cout << '=';
        else if (ca == 'S') {
            cout << (sz(a) < sz(b) ? '>' : '<');
        } else {
            cout << (sz(a) < sz(b) ? '<' : '>');
        }
    }else cout << (ca < cb ? '>' : '<');
    cout << '\n';
}
 
int main() {
    int t;
    cin >> t;
 
    forn(tt, t) {
        solve();
    }
}

#include "bits/stdc++.h"
using namespace std;

void solve(){
    int n;
    cin >> n;
    if(n == 3){
        cout << -1 << endl;
    }
    else{
        for(int i = 3; i <= n; i++) cout << i << ' ';
        cout << 2 << ' ' << 1 << endl;
    }
}

int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 2020;

int n;
int arr[MAXN];

int go(int i, int sum) {
	if (i == n) return 0;
	for (int j = i + 1, cur = 0; j <= n; ++j) {
		cur += arr[j - 1];
		if (cur > sum) return n;
		if (cur == sum) return max(j - i, go(j, sum));
	}
	return n;
}

int solve() {
	int ans = n;
	for (int len = 1, sum = 0; len < n; ++len) {
		sum += arr[len - 1];
		ans = min(ans, go(0, sum));
	}
	return ans;
}

int main() {
	int t; cin >> t;
	while (t--) {
		cin >> n;
		for (int i = 0; i < n; ++i)
			cin >> arr[i];
		cout << solve() << endl;
	}
}

#include <bits/stdc++.h>

using namespace std;

const int MAXM = 300300;

int n, m;
int arr[MAXM];

int solve(int l, int r) {
	if (r - l == 1) return 0;
	int mid = (l + r) >> 1;
	int mal = *max_element(arr + l, arr + mid);
	int mar = *max_element(arr + mid, arr + r);
	int ans = 0;
	if (mal > mar) {
		++ans;
		for (int i = 0; i < (mid - l); ++i)
			swap(arr[l + i], arr[mid + i]);
	}
	return solve(l, mid) + solve(mid, r) + ans;
}

int solve() {
	int ans = solve(0, m);
	if (is_sorted(arr, arr + m))
		return ans;
	return -1;
}

int main() {
	int t; cin >> t;
	while (t--) {
		cin >> m;
		for (int i = 0; i < m; ++i)
			cin >> arr[i];
		cout << solve() << endl;
	}
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back



void solve() {
    int n; cin >> n;
    vector<int> a(n+1);
    for (int i = 1; i <= n; ++i) {
        cin >> a[i];
    }

    vector<bool> dp(n+1, false);
    dp[0] = true;
    for (int i = 1; i <= n; ++i) {
        if (i + a[i] <= n && dp[i-1]) dp[i + a[i]] = true;
        if (i - a[i] - 1 >= 0 && dp[i - a[i] - 1]) dp[i] = true;
    }
    cout << (dp[n] ? "YES" : "NO") << '\n';
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <queue>

using namespace std;

int n;

vector<int> calc(vector<vector<int>> a) {
    vector<pair<int, int>> l(n), r(n);
    for (int i = 0; i < n; ++i) {
        l[i] = {a[i][0], i};
        r[i] = {a[i][1], i};
    }
    sort(l.begin(), l.end());
    sort(r.begin(), r.end());
    vector<vector<pair<int, int>>> suf(n);
    vector<pair<int, int>> curr;
    for (int i0 = n - 1; i0 >= 0; --i0) {
        int xr = r[i0].first;
        int i = r[i0].second;
        int xl = a[i][0];
        int c = a[i][2];
        if (curr.empty()) {
            curr.emplace_back(xl, c);
        } else if (curr.size() == 1) {
            if (curr[0].second == c) {
                curr[0].first = min(curr[0].first, xl);
            } else {
                curr.emplace_back(xl, c);
            }
        } else {
            if (curr[0].second == c) {
                curr[0].first = min(curr[0].first, xl);
            } else if (curr[1].second == c) {
                curr[1].first = min(curr[1].first, xl);
            } else {
                curr.emplace_back(xl, c);
            }
        }
        sort(curr.begin(), curr.end());
        if (curr.size() == 3) {
            curr.pop_back();
        }
        suf[i0] = curr;
    }
    vector<int> ans(n, 1e9);
    int j = 0;
    for (int i0 = 0; i0 < n; ++i0) {
        int xl = l[i0].first, i = l[i0].second;
        int xr = a[i][1], c = a[i][2];
        while (j < n && r[j].first < xl) {
            j++;
        }
        if (j < n) {
            vector<pair<int, int>> s = suf[j];
            if (s[0].second != c) {
                ans[i] = min(ans[i], max(0, s[0].first - xr));
            } else if (s.size() == 2) {
                ans[i] = min(ans[i], max(0, s[1].first - xr));
            }
        }
    }
    return ans;
}

const int K = 1e9 + 1;

void solve() {
    cin >> n;
    vector<vector<int>> a(n, vector<int>(3)), b(n, vector<int>(3));
    vector<pair<int, int>> l(n), r(n);
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < 3; ++j) {
            cin >> a[i][j];
            if (j == 2) {
                b[i][j] = a[i][j];
            } else {
                b[i][1 - j] = K - a[i][j];
            }
        }
    }
    vector<int> ans1 = calc(a), ans2 = calc(b);
    for (int i = 0; i < n; ++i) {
        cout << min(ans1[i], ans2[i]) << ' ';
    }
    cout << '\n';
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    int t = 1;
    cin >> t;
    for (int it = 0; it < t; ++it) {
        solve();
    }
    return 0;
}

from collections import deque
 
 
def solve():
    n, m = map(int, input().split())
    sl = [[] for _ in range(n)]
    for _ in range(m):
        u, v = map(int, input().split())
        u -= 1
        v -= 1
        sl[u] += [v]
        sl[v] += [u]
    f = int(input())
    h = [int(x) - 1 for x in input().split()]
    mask = [0] * n
    k = int(input())
    p = [int(x) - 1 for x in input().split()] + [-1]
    for i in range(k):
        mask[h[p[i]]] += 1 << i
    vars = [set() for _ in range(n)]
    dist = [-1] * n
    dist[0] = 0
    vars[0].add(mask[0])
    q = deque([0])
    while len(q) > 0:
        v = q.popleft()
        for u in sl[v]:
            if dist[u] == -1:
                dist[u] = dist[v] + 1
                q.append(u)
            if dist[u] == dist[v] + 1:
                for msk in vars[v]:
                    vars[u].add(msk | mask[u])
    backpack = [False] * (1 << k)
    backpack[0] = True
    j = 0
    for i in range(f):
        if i == p[j]:
            j += 1
            continue
        nw = backpack.copy()
        for msk in range(1 << k):
            if not backpack[msk]:
                continue
            for var in vars[h[i]]:
                nw[msk | var] = True
        backpack, nw = nw, backpack
    mn = k
    for msk in range(1 << k):
        if not backpack[msk]:
            continue
        ans = 0
        for b in range(k):
            if msk & (1 << b) == 0:
                ans += 1
        mn = min(mn, ans)
    print(mn)
 
 
t = int(input())
for _ in range(t):
    solve()

t = int(input())
for _ in range(t):
    a, b, c = map(int, input().split())
    d1 = a - 1
    d2 = abs(b - c) + c - 1
    ans = 0
    if d1 <= d2:
        ans += 1
    if d1 >= d2:
        ans += 2
    print(ans)

#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <queue>

using namespace std;

char get(int i) {
    return 'a' + i - 1;
}

void solve() {
    int n;
    string s;
    cin >> n >> s;
    int i = n - 1;
    string res;
    while (i >= 0) {
        if (s[i] != '0') {
            res += get(s[i] - '0');
            i--;
        } else {
            res += get(stoi(s.substr(i - 2, 2)));
            i -= 3;
        }
    }
    reverse(res.begin(), res.end());
    cout << res << '\n';
}

int main() {
    int t = 1;
    cin >> t;
    for (int it = 0; it < t; ++it) {
        solve();
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

#define forn(i, n) for (int i = 0; i < int(n); i++)

void solve() {

    string s;
    cin >> s;

    int n = s.size();
    map<char, vector<int>> let_to_ind;

    for (int i = 0; i < n; ++i) {
        let_to_ind[s[i]].push_back(i);
    }

    int direction = (s[0] < s[n - 1]) ? 1 : -1;
    vector<int> ans;

    for (char c = s[0]; c != s[n - 1] + direction; c += direction) {
        for (auto now : let_to_ind[c]) {
            ans.push_back(now);
        }
    }

    int cost = 0;
    for (int i = 1; i < ans.size(); i++)
        cost += abs(s[ans[i]] - s[ans[i - 1]]);

    cout << cost << " " << ans.size() << '\n';
    for (auto now : ans) {
        cout << now + 1 << " ";
    }
    cout << '\n';
}
int main() {
    int tests;
    cin >> tests;
    forn(tt, tests) {
        solve();
    }
}

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

void solve(){
    int n;
    cin >> n;
    vector<ll>x(n), y(n);
    vector<pair<ll, int>>dif(n);

    for(auto &i : x) cin >> i;
    for(auto &i: y) cin >> i;
    for(int i = 0; i < n; i++){
        dif[i].first = y[i] - x[i];
        dif[i].second = i;
    }
    sort(dif.begin(), dif.end());
    reverse(dif.begin(), dif.end());

    int j = n - 1, cnt = 0;

    for(int i = 0; i < n; i++){
        while(j > i && dif[i].first + dif[j].first < 0) j--;
        if(j <= i) break;
        cnt++; j--;
    }
    cout << cnt << endl;
}

int main() {
    int t;
    cin >> t;
    while(t--){
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back

long long ask(int a, int b) {
    cout << "? " << a << ' ' << b << endl;
    long long x; cin >> x;
    return x;
}

long long solve() {
    for (int i = 2; i <= 26; i++) {
        long long x = ask(1, i);
        long long y = ask(i, 1);
        if (x == -1) return i-1;
        if (x != y) return x + y;
    }
    assert(false);
}

int main() {
    long long ans = solve();
    cout << "! " << ans << endl;
}

#include <bits/stdc++.h>

#define endl '\n'

using namespace std;

typedef pair<int, int> ipair;

const int MAXSZ = 200200;
const int INF = 2e9;

inline int add(int a, int b) {
	return (a + b >= 9 ? a + b - 9 : a + b);
}

inline int sub(int a, int b) {
	return (a < b ? a + 9 - b : a - b);
}

inline int mul(int a, int b) {
	return a * b % 9;
}

int sz, n, m;
string s;
int ps[MAXSZ];
vector<int> D[9];

void build() {
	sz = s.size();
	for (int md = 0; md < 9; ++md)
		D[md].clear();
	for (int i = 0; i < sz; ++i)
		ps[i + 1] = ps[i] + (s[i] - '0');
	for (int i = 0; i + n <= sz; ++i)
		D[(ps[i + n] - ps[i]) % 9].push_back(i);
}

ipair solve(int l, int r, int k) {
	int x = (ps[r] - ps[l]) % 9;
	ipair ans {INF, INF};
	for (int a = 0; a < 9; ++a) {
		int b = sub(k, mul(a, x));
		if (D[a].empty() || D[b].empty()) continue;
		if (a != b)
			ans = min(ans, make_pair(D[a].front(), D[b].front()));
		else if (D[a].size() >= 2)
			ans = min(ans, make_pair(D[a].front(), D[a][1]));
	}
	if (ans == make_pair(INF, INF))
		return {-2, -2};
	return ans;
}

int main() {
	ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
	int t; cin >> t;
	while (t--) {
		cin >> s >> n >> m;
		build();
		for (int i = 0; i < m; ++i) {
			int l, r, k; cin >> l >> r >> k, --l;
			auto [ans1, ans2] = solve(l, r, k);
			cout << ++ans1 << ' ' << ++ans2 << endl;
		}
	}
}

#include<cstdio>
#include<cstring>
const int N=505;
const int Mod=1e9+7;
char s[N],t[N];
int n,m;
int f[N],g[N];
int p[N],tot;
inline void Init(){
	scanf("%s",s+1);
	scanf("%s",t+1);
	n=strlen(s+1);
	m=strlen(t+1);
	tot=0;
	for(int i=1;i+m-1<=n;i++){
		bool flg=1;
		for(int j=1;j<=m;j++)
			if(s[i+j-1]!=t[j]) flg=0;
		if(flg) p[++tot]=i;
	}
	return ;
}
inline int addv(int x,int y){
	int s=x+y;
	if(s>=Mod) s-=Mod;
	return s;
}
inline int subv(int x,int y){
	int s=x-y;
	if(s<0) s+=Mod;
	return s;
}
inline void add(int&x,int y){
	x=addv(x,y);
	return ;
}
inline void sub(int&x,int y){
	x=subv(x,y);
	return ;
}
inline void Solve(){
	memset(f,0x3f,sizeof(f));
	memset(g,0,sizeof(g));
	p[0]=-N;
	f[0]=0;
	g[0]=1;
	p[++tot]=n+m;
	for(int i=0;i<tot;i++){
		int j=i+1;
		while(j<=tot&&p[j]<=p[i]+m-1) j++;
		for(int k=j;p[j]+m-1>=p[k]&&k<=tot;k++){
			if(f[i]+1<f[k]){
				f[k]=f[i]+1;
				g[k]=g[i];
			}
			else if(f[i]+1==f[k]) add(g[k],g[i]);
		}
	}
	printf("%d %d\n",f[tot]-1,g[tot]);
	return ;
}
int T;
int main(){
	for(scanf("%d",&T);T;T--){
		Init();
		Solve();
	}
	return 0;
}

#include <bits/stdc++.h>

#define int long long
#define pb emplace_back
#define mp make_pair
#define x first
#define y second
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

typedef long double ld;
typedef long long ll;

using namespace std;

mt19937 rnd(143);

const int inf = 1e15;
const int M = 1e9 + 7;
const ld pi = atan2(0, -1);
const ld eps = 1e-6;

void solve(){
    int n;
    cin >> n;
    int time, h, m;
    cin >> h >> m;
    time = 60 * h + m;
    int ans = 24 * 60;
    for(int i = 0; i < n; ++i){
        cin >> h >> m;
        int t = 60 * h + m - time;
        if(t < 0) t += 24 * 60;
        ans = min(ans, t);
    }
    cout << ans / 60 << " " << ans % 60;
}

bool multi = true;

signed main() {
    int t = 1;
    if (multi)cin >> t;
    for (; t; --t) {
        solve();
        cout << endl;
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)

int main() {
    int t;
    cin >> t;
    forn(tt, t) {
        int n;
        cin >> n;
        vector<int> a(n);
        forn(i, n)
            cin >> a[i];
        bool yes = false;
        set<int> c;
        for (int i = n - 1; i >= 0; i--) {
            if (c.count(a[i])) {
                cout << i + 1 << endl;
                yes = true;
                break;
            }
            c.insert(a[i]);
        }
        if (!yes)
            cout << 0 << endl;
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)

int main() {
    int t;
    cin >> t;
    forn(tt, t) {
        int s;
        cin >> s;
        string result;
        for (int d = 9; d >= 1; d--)
            if (s >= d) {
                result = char('0' + d) + result;
                s -= d;
            }
        cout << result << endl;
    }
}

#include<bits/stdc++.h>
#define len(s) (int)s.size()
#define forn(i, n) for (int i = 0; i < int(n); i++)

using namespace std;
int ans = 0;
bool ok = true;

void Find(int a, int b, string &t, vector<string>&str, vector<pair<int, int>>&match){
    int Max = 0, id = -1, pos = -1;
    for(int i = a; i <= b; i++){
        for(int j = 0; j < len(str); j++){
            string s = str[j];
            if(i + len(s) > len(t) || i + len(s) <= b) continue;
            if(t.substr(i, len(s)) == s) {
                if(i + len(s) > Max){
                    Max = i + len(s);
                    id = j;
                    pos = i;
                }
            }
        }
    }
    if(id == -1) {
        ok = false;
        return;
    }
    else{
        match.emplace_back(id, pos);
        ans++;
        if(Max == len(t)) return;
        else Find(max(pos + 1, b +1), Max, t, str, match);
    }
}


void solve(){
    ans = 0;
    ok = true;

    string t;
    cin >> t;
    int n;
    cin >> n;

    vector<string>s(n);
    vector<pair<int, int>>match;

    forn(i, n) {
        cin >> s[i];
    }

    Find(0, 0, t, s, match);
    if(!ok) cout << "-1\n";
    else{
        cout << ans << endl;
        for(auto &p : match) cout << p.first + 1 << ' ' << p.second + 1 << endl;
    }

}

int main(){
    int q;
    cin >> q;
    while(q--){
        solve();
    }
    return 0;
}

#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <queue>

using namespace std;

int next(int x) {
    return x + x % 10;
}

void solve() {
    int n;
    cin >> n;
    vector<int> a(n);
    bool flag = false;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
        if (a[i] % 5 == 0) {
            flag = true;
            a[i] = next(a[i]);
        }
    }
    if (flag) {
        cout << (*min_element(a.begin(), a.end()) == *max_element(a.begin(), a.end()) ? "Yes": "No") << '\n';
    } else {
        bool flag2 = false, flag12 = false;
        for (int i = 0; i < n; ++i) {
            int x = a[i];
            while (x % 10 != 2) {
                x = next(x);
            }
            if (x % 20 == 2) {
                flag2 = true;
            } else {
                flag12 = true;
            }
        }
        cout << ((flag2 & flag12) ? "No" : "Yes") << '\n';
    }
}

int main() {
    int t = 1;
    cin >> t;
    for (int it = 0; it < t; ++it) {
        solve();
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)

int main() {
    int t;
    cin >> t;
    forn(tt, t) {
        int n;
        cin >> n;
        vector<int> d(3);
        forn(i, 3)
            cin >> d[i];
        int sum = d[0] + d[1] + d[2];
        if (sum % 2 == 0) {
            vector<int> w(3);
            forn(i, 3)
                w[i] = sum / 2 - d[(i + 1) % 3];
            vector<int> sw(w.begin(), w.end());
            sort(sw.begin(), sw.end());
            if (sw[0] >= 0 && sw[1] >= 1) {
                vector<pair<int,int>> edges;
                int num = 3;
                int center;
                if (sw[0] == 0)
                    center = min_element(w.begin(), w.end()) - w.begin();
                else
                    center = num++;
                forn(i, 3) {
                    int before = center;
                    forn(j, w[i] - 1) {
                        edges.push_back({before, num});
                        before = num++;
                    }
                    if (w[i] > 0)
                        edges.push_back({before, i});
                }
                if (num <= n) {
                    while (num < n)
                        edges.push_back({center, num++});
                    cout << "YES" << endl;
                    for (auto& [u, v]: edges)
                        cout << u + 1 << " " << v + 1 << endl;
                    continue;
                }
            }
        }
        cout << "NO" << endl;
    }
}

#pragma GCC optimize("O3","unroll-loops")
#pragma GCC target("avx2")
#include <bits/stdc++.h>

using namespace std;
#define int long long

const int maxn=2e5+5;
vector<int> ch[maxn];
int a[maxn];
int b[maxn];
int ans[maxn];
vector<int> vb;
int curb=0;
int cura=0;

void dfs(int x){
    curb+=b[x];
    cura+=a[x];
    vb.push_back(curb);
    ans[x]=upper_bound(vb.begin(),vb.end(),cura)-vb.begin();
    for(int v:ch[x]){
        dfs(v);
    }
    curb-=b[x];
    cura-=a[x];
    vb.pop_back();
}
int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    int t;
    cin>>t;
    while(t--){
        int n;cin>>n;
        for(int i=0;i<n;++i) ch[i].clear();
        for(int i=1;i<n;++i){
            int pr,a1,b1;
            cin>>pr>>a1>>b1;
            --pr;
            ch[pr].push_back(i);
            a[i]=a1;
            b[i]=b1;
        }
        dfs(0);
        for(int i=1;i<n;++i) cout<<ans[i]-1<<' ';
        cout<<'\n';
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back



void solve() {
    int m; cin >> m;
    string t = to_string(m);
    string s = "1";
    for (int i = 1; i < sz(t); i++) {
        s += '0';
    }
    int k = stoi(s);
    cout << m - k << '\n';
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back



void solve() {
    string s; cin >> s;
    set<char> v;
    int ans = 0;
    for (int i = 0; i < sz(s); i++) {
        v.insert(s[i]);
        if (sz(v) > 3) {
            ans++;
            v.clear();
            v.insert(s[i]);
        }
    }
    if (!v.empty()) ans++;
    cout << ans << endl;
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include<bits/stdc++.h>
using namespace std;
#define forn(i, n) for (int i = 0; i < int(n); i++)


void solve(){
    int n, k;
    cin >> n >> k;
    map<int, pair<int, int>>m;
    forn(i, n){
        int u;
        cin >> u;
        if(!m.count(u)) {
            m[u].first = i;
            m[u].second = i;
        }
        else m[u].second = i;
    }
    forn(i, k){
        int a, b;
        cin >> a >> b;
        if(!m.count(a) or !m.count(b) or m[a].first > m[b].second) {
            cout << "NO\n"; //equals = 0 = wrong
        }
        else cout << "YES\n";
    }
}

int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)

int main() {
    int t;
    cin >> t;
    forn(tt, t) {
        string s;
        cin >> s;
        int p;
        cin >> p;
        string w(s);
        sort(w.rbegin(), w.rend());
        int cost = 0;
        forn(i, s.length())
            cost += s[i] - 'a' + 1;
        map<char,int> del;
        forn(i, w.length())
            if (cost > p) {
                del[w[i]]++;
                cost -= w[i] - 'a' + 1;
            }
        forn(i, s.length()) {
            if (del[s[i]] > 0) {
                del[s[i]]--;
                continue;
            }
            cout << s[i];
        }
        cout << endl;
    }
}

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

#define forn(i, n) for (int i = 0; i < int(n); i++)

map<int, vector<int>> m;
vector<bool> used;

int go(int v) {
    used[v] = true;
    for (auto now : m[v]) {
        if (!used[now]) {
            return go(now) + 1;
        }
    }
    return 1;
}

void solve() {

    int n, x, y;
    cin >> n;

    m.clear();
    used.clear();
    used.resize(n + 1, false);

    bool fault = false;
    forn(i, n) {
        cin >> x >> y;
        m[x].push_back(y);
        m[y].push_back(x);
        if (x == y || m[x].size() > 2 || m[y].size() > 2) fault = true;
    }

    if (fault) {
        cout << "NO\n";
        return;
    }

    forn(i, n) {
        if (!used[i + 1]) {
            if (go(i + 1) % 2) {
                cout << "NO\n";
                return;
            }
        }
    }

    cout << "YES\n";
}
int main() {
    int tests;
    cin >> tests;
    forn(tt, tests) {
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back

const int INF = 1e9;

void solve() {
    int n; cin >> n;
    multiset<int> a, b;

    forn(i, n) {
        int x; cin >> x;
        while (x % 2 == 0) {
            x /= 2;
        }
        a.insert(x);
    }

    forn(i, n) {
        int x; cin >> x;
        b.insert(x);
    }
    n = sz(a);

    while (!b.empty()) {
        int x = *b.rbegin();
        // cout << x << endl;
        if (!a.count(x)) {
            if (x == 1) break;
            b.erase(b.find(x));
            b.insert(x / 2);
        } else {
            b.erase(b.find(x));
            a.erase(a.find(x));
        }
    }

    cout << (b.empty() ? "YES" : "NO") << endl;

}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include <bits/stdc++.h>

#define int long long
#define pb emplace_back
#define mp make_pair
#define x first
#define y second
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

typedef long double ld;
typedef long long ll;

using namespace std;

mt19937 rnd(143);

const int inf = 1e15;
const int M = 1e9 + 7;
const ld pi = atan2(0, -1);
const ld eps = 1e-6;

void depth(int v, int p, vector<vector<int>> &sl, vector<int> &d){
    if(p >= 0) d[v] = d[p] + 1;
    for(int u: sl[v]){
        if(u == p) continue;
        depth(u, v, sl, d);
    }
}

int dfs(int v, int p, vector<vector<int>> &sl, vector<bool> &chosen){
    int res = 0;
    bool lower = false;
    for(int u: sl[v]){
        if(u == p) continue;
        res += dfs(u, v, sl, chosen);
        lower = lower || chosen[u];
    }
    chosen[v] = chosen[v] || lower;
    if(chosen[v] && !lower) res = 1;
    return res;
}

void solve(){
    int n;
    cin >> n;
    vector<vector<int>> sl(n);
    for(int i = 1; i < n; ++i){
        int u, v;
        cin >> u >> v;
        sl[--u].push_back(--v);
        sl[v].push_back(u);
    }
    vector<int> d(n);
    depth(0, -1, sl, d);
    int q;
    cin >> q;
    for(; q; --q){
        int k;
        cin >> k;
        vector<bool> chosen(n);
        int mx = 0;
        for(int i = 0; i < k; ++i){
            int p;
            cin >> p;
            --p;
            if(d[p] > d[mx]) mx = p;
            chosen[p] = true;
        }
        int leaves = dfs(mx, -1, sl, chosen);
        if(leaves == 1) cout << "YES\n";
        else cout << "NO\n";
    }
}

bool multi = false;

signed main() {
    int t = 1;
    if (multi)cin >> t;
    for (; t; --t) {
        solve();
        //cout << endl;
    }
    return 0;
}

#include <bits/stdc++.h>

#define int long long
#define pb emplace_back
#define mp make_pair
#define x first
#define y second
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

typedef long double ld;
typedef long long ll;

using namespace std;

mt19937 rnd(143);

const int inf = 1e15;
const int M = 1e9 + 7;
const ld pi = atan2(0, -1);
const ld eps = 1e-6;

int n, sz;
vector<vector<int>> sl, up;
vector<int> d;

void precalc(int v, int p){
    d[v] = d[p] + 1;
    up[v][0] = p;
    for(int i = 1; i <= sz; ++i){
        up[v][i] = up[up[v][i - 1]][i - 1];
    }
    for(int u: sl[v]){
        if(u == p) continue;
        precalc(u, v);
    }
}

int lca(int u, int v){
    if(d[u] < d[v]){
        swap(u, v);
    }
    for(int cur = sz; cur >= 0; --cur){
        if (d[u] - (1 << cur) >= d[v]) {
            u = up[u][cur];
        }
    }
    for(int cur = sz; cur >= 0; --cur){
        if (up[u][cur] != up[v][cur]) {
            u = up[u][cur];
            v = up[v][cur];
        }
    }
    return u == v ? u : up[u][0];
}

void solve(){
    cin >> n;
    sz = 0;
    while ((1 << sz) < n) sz++;
    d.assign(n, -1);
    up.assign(n, vector<int>(sz + 1));
    sl.assign(n, vector<int>(0));
    for(int i = 1; i < n; ++i){
        int u, v;
        cin >> u >> v;
        sl[--u].push_back(--v);
        sl[v].push_back(u);
    }
    precalc(0, 0);
    int q;
    cin >> q;
    for(; q; --q){
        int k;
        cin >> k;
        vector<int> p(k);
        for(int &e: p) {
            cin >> e;
            --e;
        }
        sort(all(p), [](int a, int b) {
            return d[a] > d[b];
        });
        vector<bool> used(k);
        for(int i = 0; i < k; ++i){
            if(lca(p[0], p[i]) == p[i]) used[i] = true;
        }
        int f = 0;
        while (f < k && used[f]) f++;
        if(f == k){
            cout << "YES\n";
            continue;
        }
        bool ans = true;
        for(int i = f; i < k; ++i){
            if(lca(p[f], p[i]) == p[i]) used[i] = true;
        }
        for(bool e: used){
            ans &= e;
        }
        ans &= d[lca(p[0], p[f])] <= d[p.back()];
        if(ans) cout << "YES\n";
        else cout << "NO\n";
    }
}

bool multi = false;

signed main() {
    int t = 1;
    if (multi)cin >> t;
    for (; t; --t) {
        solve();
        //cout << endl;
    }
    return 0;
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)

int main() {
    int t;
    cin >> t;
    forn(tt, t) {
        int a, b, c, x, y;
        cin >> a >> b >> c >> x >> y;
        int ax = min(a, x);
        int by = min(b, y);
        a -= ax;
        x -= ax;
        b -= by;
        y -= by;
        if (c >= x + y)
            cout << "YES" << endl;
        else
            cout << "NO" << endl;
    }
}

#include<bits/stdc++.h>
using namespace std;
void solve(){
    int n;
    cin >> n;
    vector<int>a(n);
    for(auto &i : a) cin >> i;
    int ans = 0;
    for(int i = n - 2; i >= 0; i--){
        while(a[i] >= a[i + 1] && a[i] > 0){
            a[i] /= 2;
            ans++;
        }
        if(a[i] == a[i+1]){
            cout << -1 << '\n';
            return;
        }
    }
    cout << ans << '\n';
}
int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)

int main() {
    int t;
    cin >> t;
    forn(tt, t) {
        string s;
        cin >> s;
        int n = s.length();
        vector<bool> a(n + 1);
        a[0] = true;
        forn(i, n)
            a[i + 1] = a[i] && (s[i] == '1' || s[i] == '?');
        vector<bool> b(n + 1);
        b[0] = true;
        for (int i = n - 1; i >= 0; i--)
            b[n - i] = b[n - i - 1] && (s[i] == '0' || s[i] == '?');
        int result = 0;
        forn(i, n)
            if (a[i] && b[n - i - 1])
                result++;
        cout << result << endl;
    }
}

#include<bits/stdc++.h>
using namespace std;

void solve(){
    int n;
    cin >> n;
    vector<int>b(n + 1);
    vector<bool>leaf(n + 1, true);
    for(int i = 1; i <= n; i++) {
        cin >> b[i];
        leaf[b[i]] = false;
    }

    if(n == 1){
        cout << "1\n1\n1\n\n";
        return;
    }

    vector<int>paths[n + 1];
    vector<bool>used(n + 1, false);
    int color = 0;

    for(int i = 1; i <= n; i++){
        if(!leaf[i]) continue;
        used[i] = true;
        paths[color].emplace_back(i);

        int v = i;
        while (b[v] != v && !used[b[v]]){
            v = b[v];
            used[v] = true;
            paths[color].emplace_back(v);
        }
        color++;
    }

    cout << color << '\n';
    for(auto &path : paths){
        if(path.empty()) continue;
        cout << (int)path.size() << '\n';
        reverse(path.begin(), path.end());
        for(auto &v: path) cout << v << ' ';
        cout << '\n';
    }
    cout << '\n';
}
int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

#define forn(i, n) for (int i = 0; i < int(n); i++)
#define sz(v) (int)v.size()
#define all(v) v.begin(),v.end()
#define eb emplace_back

template <class T> bool ckmax(T &a, T b) {return a<b ? a=b, true : false;}


void solve() {
    int n,k; cin >> n >> k;
    string s; cin >> s;

    char mn = 'a';
    for (int i = 0; i < n; i++) if(s[i] > mn) {
        if (s[i] - 'a' > k) {
            k -= mn - 'a';
            int to = s[i] - k;
            for (char c = s[i]; c > to; c--) {
                for (char &e:s) if (e == c) {
                    e = char(c-1);
                }
            }
            break;
        } else ckmax(mn, s[i]);
    }
    for (char &e:s) if (e <= mn) {
        e = 'a';
    }
    cout << s << endl;
}

int main() {
    int t;
    cin >> t;

    forn(tt, t) {
        solve();
    }
}

#include <bits/stdc++.h>

using namespace std;

//#define int long long
#define ll long long
//#define double long double
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

const int MOD = 1e9 + 7;
const int maxN = 5e3 + 1;
const int INF = 2e9;
const int MB = 20;

vector<vector<int>> g;
vector<bool> todo, good;

void dfs(int v, int p = -1) {
    for (int u : g[v]) {
        if (u != p) {
            dfs(u, v);
            if (todo[u]) {
                todo[v] = true;
            }
            if (good[u]) {
                good[v] = true;
            }
        }
    }
}

void solve() {
    int n, k;
    cin >> n >> k;
    g.clear();
    g.resize(n);
    int x, y;
    cin >> x >> y;
    --x;
    --y;
    todo.resize(n);
    fill(all(todo), false);
    good.resize(n);
    fill(all(good), false);
    for (int i = 0; i < k; ++i) {
        int v;
        cin >> v;
        --v;
        todo[v] = true;
    }
    good[y] = true;
    for (int i = 0; i < n - 1; ++i) {
        int v, u;
        cin >> v >> u;
        --v;
        --u;
        g[v].push_back(u);
        g[u].push_back(v);
    }
    dfs(x);
    int ans = 0;
    for (int i = 0; i < n; ++i) {
        if (i == x) {
            continue;
        }
        if (good[i]) {
            ++ans;
        } else if (todo[i]) {
            ans += 2;
        }
    }
    cout << ans << '\n';
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    //    srand(time(0));
    int t = 1;
    cin >> t;
    while (t--) solve();
}

#include <bits/stdc++.h>

//#define int long long
#define mp make_pair
#define x first
#define y second
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()

typedef long double ld;
typedef long long ll;

using namespace std;

mt19937 rnd(143);

const ll inf = 1e9 + 7;
const ll M = 998'244'353;
const ld pi = atan2(0, -1);
const ld eps = 1e-4;

void solve(int test_case) {
    int n, m;
    cin >> n >> m;
    vector<int> a(n), pancakes(1);
    for(int &e: a) cin >> e;
    for(int i = 0; i < n; ++i){
        for(int j = 0; j < a[i]; ++j){
            pancakes.emplace_back(i);
            int c = pancakes.size();
            pancakes[c - 1] += pancakes[c - 2];
        }
        if(i > 0) a[i] += a[i - 1];
    }
    vector<vector<vector<int>>> dp(n, vector<vector<int>>(m + 1, vector<int>(m + 1, inf)));
    for(int j = 0; j <= m; j++){
        if(a[0] >= j) dp[0][j][j] = a[0] - j;//moved right
        else dp[0][j][j] = pancakes[j];//moved from right
    }
    for(int j = m - 1; j >= 0; --j){
        for(int k = j; k <= m; ++k){
            dp[0][j][k] = min(dp[0][j][k], dp[0][j + 1][k]);
        }
    }
    for(int i = 1; i < n; ++i){
        for(int j = 0; j <= m; ++j){
            for(int k = j; k <= m; ++k){
                int add = 0;
                if(a[i] >= k) add = a[i] - k;//moved to i + 1
                else {
                    int lend = min(j, k - a[i]);
                    add = pancakes[k] - pancakes[k - lend] - i * (lend);//moved from greater i
                }
                dp[i][j][k] = dp[i - 1][j][k - j] + add;
            }
        }

        for(int j = m - 1; j >= 0; --j){
            for(int k = (i + 1) * j; k <= m; ++k){
                dp[i][j][k] = min(dp[i][j][k], dp[i][j + 1][k]);
            }
        }
    }
    cout << dp[n-1][0][m];
}

bool multi = false;

signed main() {
    int t = 1;
    if (multi) {
        cin >> t;
    }
    for (int i = 1; i <= t; ++i) {
        solve(i);
        cout << "\n";
    }
    return 0;
}