I understood the tutorial O(n.sqrt(n)) solution, but can't seem to understand why my solution with the same complexity is exceeding the time limit. Any help would be greatly appreciated!

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

#define ll long long
#define err() cout << "==================" << endl;
#define err1(a) cout << #a << " " << a << endl;
#define err2(a, b) cout << #a << " " << a << " " << #b << " " << b << endl;
#define err3(a, b, c) cout << #a << " " << a << " " << #b << " " << b << " " << #c << " " << c << " " << endl;
const ll mod = 998244353;

void solve(int testCase) {
    ll i = 1, j, n, k;
    cin >> n >> k;
    vector<ll> dp1(n + 1, 0), dp2(n + 1, 0), ans(n + 1, 0);
    dp1[0] = 1;
    ans[0] = 1;
    for (i = 1; k * i + ((i * (i - 1)) / 2) <= n; i++) {
        for (j = 0; j <= n; j++) {
            if (j - (k + i - 1) >= 0) {
                dp1[j] = (dp1[j] + dp1[j - (k + i - 1)]) % mod;
                dp2[j] = dp1[j - (k + i - 1)] % mod;
            }
        }
        for (j = 0; j <= n; j++) {
            ans[j] = (ans[j] + dp2[j]) % mod;
            dp1[j] = dp2[j] % mod;
            dp2[j] = 0;
        }
    }
    for (i = 1; i <= n; i++) cout << ans[i] % mod << " ";
    cout << endl;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll t = 1;
    // cin >> t;
    for (int testCase = 1; testCase <= t; testCase++)
        solve(testCase);
    return 0;
}

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