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#include<bits/stdc++.h>
#define pb push_back
#define fast ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define ll long long
#define pii pair<int,int>
#define pll pair<ll,ll>
#define f first
#define s second
#define int long long
#define sz(x) (ll)(x.size())
using namespace std;


const int mod = 1e9+7;

int expo_pow(int x,int y){
 if(y == 0) return 1;
  y=y%(mod-1);
  x%=mod;
  if(y==0) y=mod-1;
  int res=1;
  while(y){
    if(y&1) res=(res*x)%mod;
    x=(x*x)%mod;
    y>>=1; 
  }
  return res;
}

ll add()
{
    return 0;
}

template <typename T, typename... Types>
T add(T var1, Types... var2){
    return (((((ll)(var1)) % mod + (ll)(add(var2...))) % mod) + mod) % mod;
}

ll mul(){
    return 1;
}

template <typename T, typename... Types>
T mul(T var1, Types... var2){
    return (((ll)(var1)) % mod * (ll)(mul(var2...))) % mod;
}

int n,m;
vector<vector<int>> adj;
int cnt_cric,bridges;
vector<vector<int>> adj2;
vector<bool> visited;
vector<int> tin,low;
vector<bool> is_cut;
int timer,comp,mx_comp;
int cur_comp;
int cut_count = 0;
vector<vector<bool>> done;

void init() {
  adj.clear();
  adj.resize(n+1);
  adj2.clear();
  adj2.resize(n+1);
  tin.clear();
  tin.resize(n+1);
  low.clear();
  low.resize(n+1);
  visited.clear();
  visited.assign(n+1,0);
  is_cut.clear();
  is_cut.assign(n+1,0);
  done.clear();
  done.assign(n+1,vector<bool>(n+1,0));
  cnt_cric = 0;
  bridges = 0;
  timer = 0;
  comp = 0;
  mx_comp = 0;
}

void dfs(int v,int p = -1) {
  visited[v] = 1;
  tin[v] = low[v] =timer++;
  int children = 0;

  for (auto u:adj[v]) {
    if (u == p) continue;
    if (visited[u]) {
      if (done[u][v] == 0) {
        adj2[u].pb(v);
        adj2[v].pb(u);
        done[u][v] = 1;
        done[v][u] = 1;
      }
      low[v] = min(tin[u],low[v]);
    }
    else {
      dfs(u,v);
      low[v] = min(low[u],low[v]);

      if (low[u] >= tin[v] and p != -1) {
        is_cut[v] = 1;
      }
      if (low[u] > tin[v]) {
        bridges++;
      } else {
        if (done[u][v] == 0) {
          adj2[u].pb(v);
          adj2[v].pb(u);
          done[u][v] = 1;
          done[v][u] = 1;
        }
      }

      ++children;
    }
  }

  if (p == -1 and children > 1) {
    is_cut[v] = 1;
  }
}

void dfs2(int cur,int par = -1) {
  if (is_cut[cur] == 1 and cut_count == 0){
    cut_count++;
    return;
  }
  visited[cur] = 1;
  for (auto u:adj2[cur]) {
    if (u == par) continue;
    if (visited[u] == 1) {
      if (done[u][cur] == 0) {
        cur_comp++;
        done[u][cur] = 1;
        done[cur][u] = 1;
      }
    }
    else {
      dfs2(u,cur);
      if (done[u][cur] == 0) {
        cur_comp++;
        done[u][cur] = 1;
        done[cur][u] = 1;
      }
    }
  }
}

void solve(){

  cin >> n >> m;
  init();
  for (int i = 0; i < m; ++i) {
    int p,q;
    cin >> p >> q;
    adj[p].pb(q);
    adj[q].pb(p);
  }

  dfs(1);

  visited.clear();
  visited.assign(n+1,0);
  done.assign(n+1,vector<bool>(n+1,0));
  for (int i = 1; i <= n; ++i) {
    if (visited[i] == 0 and is_cut[i] == 0) {
      cut_count = 0;
      cur_comp = 0;
      dfs2(i);
      mx_comp = max(cur_comp,mx_comp);
      if(cur_comp != 0) comp++;
    } 
  }

  for (int i = 1; i <= n; ++i) {
    if (is_cut[i]) cnt_cric++;
  }

  int p = max(1LL,comp + bridges);
  int q = max(1LL,mx_comp);
  int g = __gcd(p,q);
  p /= g;
  q /= g;
  cout << cnt_cric << " " << bridges << " " << p << " " << q << "\n";
}


signed main(){
  fast;
  int test = 1;
  cin>>test;
  int i=1;
  while(test--){
    solve();
  }
}