Problem p03529 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#include <unistd.h>

using namespace std;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \
  cerr << #v << ":";                                                           \
  for (int i = 0; i < v.size(); i++)                                           \
    cerr << " " << v[i];                                                       \
  cerr << endl
#define DEBUG_MAT(v)                                                           \
  cerr << #v << endl;                                                          \
  for (int i = 0; i < v.size(); i++) {                                         \
    for (int j = 0; j < v[i].size(); j++) {                                    \
      cerr << v[i][j] << " ";                                                  \
    }                                                                          \
    cerr << endl;                                                              \
  }

typedef long long ll;

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first - t.first, s.second - t.second);
}
template <class S, class T> ostream &operator<<(ostream &os, pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = (n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const ll MOD = 1000000007;
// const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout << setprecision(15) << fixed << p << endl;
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx2[8] = {1, 1, 0, -1, -1, -1, 0, 1}, dy2[8] = {0, 1, 1, 1, 0, -1, -1, -1};
#define fio()                                                                  \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
// #define mp make_pair
// #define endl '\n'

ll mod_pow(ll x, ll p, ll M = MOD) {
  ll a = 1;
  while (p) {
    if (p % 2)
      a = a * x % M;
    x = x * x % M;
    p /= 2;
  }
  return a;
}

ll mod_inverse(ll a, ll M = MOD) { return mod_pow(a, M - 2, M); }

int n, k;
int m = 1000;

int main() {
  cin >> n >> k;
  vll p(n + 1, vl(m));
  vector<vector<vector<pll>>> zen(n + 1, vector<vector<pll>>(m));
  zen[n][0].push_back(pll(1, 0));
  for (int i = n; i >= 0; i--) {
    rep(j, m) {
      if (zen[i][j].size() == 0)
        continue;
      rep(l, zen[i][j].size()) {
        (p[i][j] += zen[i][j][l].first) %= MOD;
        ;
      }
      if (i == 0) {
        continue;
      }
      rep(x, k + 1) {
        ll nj, add;
        if (x > i) {
          nj = j;
          add = 0;
        } else {
          int ma = x + j;
          nj = j + ma / i;
          add = ma / i;
        }
        pll pdp;
        pdp.first = p[i][j] * mod_inverse(k + 1) % MOD;
        zen[i - 1][nj].push_back(pdp);
      }
    }
  }

  // DEBUG_MAT(p);
  // DEBUG_MAT(dp);

  ll ans = 0;
  rep(j, m) {
    // ans += p[0][j] * dp[0][j] % MOD;
    ans += p[0][j] * j % MOD;
    ans %= MOD;
  }

  ans = ans * mod_pow(k + 1, n) % MOD;

  ll al = 0;
  rep(x, k + 1) {
    al += x * mod_pow(k + 1, n - 1) % MOD;
    al %= MOD;
  }
  al = al * n % MOD;
  // DEBUG(al);
  ans = (al - ans + MOD) % MOD;
  cout << ans << endl;
}


Fixed submission:
#include <bits/stdc++.h>
#include <unistd.h>

using namespace std;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \
  cerr << #v << ":";                                                           \
  for (int i = 0; i < v.size(); i++)                                           \
    cerr << " " << v[i];                                                       \
  cerr << endl
#define DEBUG_MAT(v)                                                           \
  cerr << #v << endl;                                                          \
  for (int i = 0; i < v.size(); i++) {                                         \
    for (int j = 0; j < v[i].size(); j++) {                                    \
      cerr << v[i][j] << " ";                                                  \
    }                                                                          \
    cerr << endl;                                                              \
  }

typedef long long ll;

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first - t.first, s.second - t.second);
}
template <class S, class T> ostream &operator<<(ostream &os, pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = (n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const ll MOD = 1000000007;
// const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout << setprecision(15) << fixed << p << endl;
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx2[8] = {1, 1, 0, -1, -1, -1, 0, 1}, dy2[8] = {0, 1, 1, 1, 0, -1, -1, -1};
#define fio()                                                                  \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
// #define mp make_pair
// #define endl '\n'

ll mod_pow(ll x, ll p, ll M = MOD) {
  ll a = 1;
  while (p) {
    if (p % 2)
      a = a * x % M;
    x = x * x % M;
    p /= 2;
  }
  return a;
}

ll mod_inverse(ll a, ll M = MOD) { return mod_pow(a, M - 2, M); }

int n, k;
int m = 10010;

int main() {
  cin >> n >> k;
  vll p(n + 1, vl(m));
  vector<vector<vector<pll>>> zen(n + 1, vector<vector<pll>>(m));
  zen[n][0].push_back(pll(1, 0));
  for (int i = n; i >= 0; i--) {
    rep(j, m) {
      if (zen[i][j].size() == 0)
        continue;
      rep(l, zen[i][j].size()) {
        (p[i][j] += zen[i][j][l].first) %= MOD;
        ;
      }
      if (i == 0) {
        continue;
      }
      rep(x, k + 1) {
        ll nj, add;
        if (x > i) {
          nj = j;
          add = 0;
        } else {
          int ma = x + j;
          nj = j + ma / i;
          add = ma / i;
        }
        pll pdp;
        pdp.first = p[i][j] * mod_inverse(k + 1) % MOD;
        zen[i - 1][nj].push_back(pdp);
      }
    }
  }

  // DEBUG_MAT(p);
  // DEBUG_MAT(dp);

  ll ans = 0;
  rep(j, m) {
    // ans += p[0][j] * dp[0][j] % MOD;
    ans += p[0][j] * j % MOD;
    ans %= MOD;
  }

  ans = ans * mod_pow(k + 1, n) % MOD;

  ll al = 0;
  rep(x, k + 1) {
    al += x * mod_pow(k + 1, n - 1) % MOD;
    al %= MOD;
  }
  al = al * n % MOD;
  // DEBUG(al);
  ans = (al - ans + MOD) % MOD;
  cout << ans << endl;
}