Problem p03529 (C++)

Buggy submission (status: Time Limit Exceeded):
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("avx2")
//  293206GT
#include <algorithm>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <cmath>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

typedef long long ll;
#define int ll
using namespace std;
#define put(a) cout << (a) << '\n'
#define sqr(x) (x) * (x)
typedef pair<int, int> pii;
typedef long double ld;
typedef pair<int, int> pld;
typedef unsigned long long ull;

typedef vector<int> vi;
typedef vector<pii> vpii;
#define rep(x, y, a) for (int x = (y); x < (int)(a); ++x)
#define all(a) a.begin(), a.end()
#define chkmax(a, b) a = max(a, (b))
#define chkmin(a, b) a = min(a, (b))

namespace IO {

template <class A, class B>
ostream &operator<<(ostream &out, vector<pair<A, B>> a);

template <class A> ostream &operator<<(ostream &out, vector<A> a);

template <class A, class B> ostream &operator<<(ostream &out, pair<A, B> a) {
  out << a.first << " " << a.second;
  return out;
}

template <class A, class B>
ostream &operator<<(ostream &out, vector<pair<A, B>> a) {
  for (pair<A, B> x : a)
    out << x.first << " " << x.second << '\n';
  return out;
}

template <class A> ostream &operator<<(ostream &out, vector<A> a) {
  for (A x : a)
    out << x << ' ';
  return out;
}

template <class A, class B> istream &operator>>(istream &in, pair<A, B> &a) {
  in >> a.first >> a.second;
  return in;
}

template <class A> istream &operator>>(istream &in, vector<A> &a) {
  for (A &x : a)
    in >> x;
  return in;
}
} // namespace IO
using namespace IO;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int M = 1e9 + 7;
int bp(int a, int b) {
  if (b == 0)
    return 1;
  int x = bp(a, b / 2);
  x = (x * x) % M;
  if (b % 2)
    x = x * a % M;
  return x;
}
void solve() {
  int n, k;
  cin >> n >> k;
  vector<vi> dp(n + 1, vi(1e4, 0));
  rep(i, 1, n + 1) rep(j, 0, dp[i].size()) {
    rep(m, 0, k + 1) {
      int incr = (m > i ? 0 : (m + j) / i);
      if (j + incr < dp[i].size()) {
        dp[i][j] += dp[i - 1][j + incr] +
                    (m > i ? m + j : (m + j) % i) * bp(k + 1, i - 1);
        dp[i][j] %= M;
      }
    }
  }
  put(dp[n][0]);
}

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cout.precision(30);
  int q = 1;
  //    cin >> q;
  //    freopen("input.txt", "r", stdin);
  while (q--)
    solve();
}


Fixed submission:
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("avx2")
//  293206GT
#include <algorithm>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <cmath>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

typedef long long ll;
#define int ll
using namespace std;
#define put(a) cout << (a) << '\n'
#define sqr(x) (x) * (x)
typedef pair<int, int> pii;
typedef long double ld;
typedef pair<int, int> pld;
typedef unsigned long long ull;

typedef vector<int> vi;
typedef vector<pii> vpii;
#define rep(x, y, a) for (int x = (y); x < (int)(a); ++x)
#define all(a) a.begin(), a.end()
#define chkmax(a, b) a = max(a, (b))
#define chkmin(a, b) a = min(a, (b))

namespace IO {

template <class A, class B>
ostream &operator<<(ostream &out, vector<pair<A, B>> a);

template <class A> ostream &operator<<(ostream &out, vector<A> a);

template <class A, class B> ostream &operator<<(ostream &out, pair<A, B> a) {
  out << a.first << " " << a.second;
  return out;
}

template <class A, class B>
ostream &operator<<(ostream &out, vector<pair<A, B>> a) {
  for (pair<A, B> x : a)
    out << x.first << " " << x.second << '\n';
  return out;
}

template <class A> ostream &operator<<(ostream &out, vector<A> a) {
  for (A x : a)
    out << x << ' ';
  return out;
}

template <class A, class B> istream &operator>>(istream &in, pair<A, B> &a) {
  in >> a.first >> a.second;
  return in;
}

template <class A> istream &operator>>(istream &in, vector<A> &a) {
  for (A &x : a)
    in >> x;
  return in;
}
} // namespace IO
using namespace IO;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int M = 1e9 + 7;
int bp(int a, int b) {
  if (b == 0)
    return 1;
  int x = bp(a, b / 2);
  x = (x * x) % M;
  if (b % 2)
    x = x * a % M;
  return x;
}
void solve() {
  int n, k;
  cin >> n >> k;
  vector<vi> dp(n + 1, vi(4e3, 0));
  rep(i, 1, n + 1) rep(j, 0, dp[i].size()) {
    rep(m, 0, k + 1) {
      int incr = (m > i ? 0 : (m + j) / i);
      if (j + incr < dp[i].size()) {
        dp[i][j] += dp[i - 1][j + incr] +
                    (m > i ? m + j : (m + j) % i) * bp(k + 1, i - 1);
        dp[i][j] %= M;
      }
    }
  }
  put(dp[n][0]);
}

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cout.precision(30);
  int q = 1;
  //    cin >> q;
  //    freopen("input.txt", "r", stdin);
  while (q--)
    solve();
}