Problem p03832 (C++)

Buggy submission (status: Time Limit Exceeded):
// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
template <class T> using PQ = priority_queue<T>;
template <class T> using PQG = priority_queue<T, vector<T>, greater<T>>;
const int INF = 0xccccccc;
const ll LINF = 922337203685477580LL;
template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  return is >> p.first >> p.second;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << ' ' << p.second;
}

const int mod = 1000000007;
// const int mod = 998244353;

struct mint {
  int64_t x;
  mint(int64_t x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(int64_t t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) { return mint(*this) /= a; }
};

istream &operator>>(istream &is, mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

struct combination {
  vector<mint> frac, ifrac;
  combination(int n) : frac(n + 1), ifrac(n + 1) {
    assert(n < mod);
    frac[0] = 1;
    for (int i = 1; i <= n; ++i)
      frac[i] = frac[i - 1] * i;
    ifrac[n] = frac[n].inv();
    for (int i = n; i >= 1; --i)
      ifrac[i - 1] = ifrac[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return frac[n] * ifrac[k] * ifrac[n - k];
  }
} C(1000000);

#define N 1010

// head

int n, a, b, c, d;
mint dp[N][N];
bitset<N> check[N];
mint dfs(int i, int j) {
  if (check[i].test(j))
    return dp[i][j];
  check[i].set(j);
  if (i == n)
    return dp[i][j] = 1;
  if (j > d - c)
    return dp[i][j] = 0;
  mint &res = dp[i][j];
  for (int tasu = a + j; tasu <= b; tasu++) {
    mint now = C.ifrac[tasu].pow(c);
    for (int kakeru = c; kakeru <= d; kakeru++) {
      int x = tasu * kakeru + i;
      if (x > n)
        break;
      res += dfs(x, tasu - a + 1) * C.frac[n - i] * C.ifrac[n - x] * now *
             C.ifrac[kakeru];
      now *= C.ifrac[tasu];
    }
  }
  return res;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> a >> b >> c >> d;
  cout << dfs(0, 0) << endl;
}

Fixed submission:
// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
template <class T> using PQ = priority_queue<T>;
template <class T> using PQG = priority_queue<T, vector<T>, greater<T>>;
const int INF = 0xccccccc;
const ll LINF = 922337203685477580LL;
template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  return is >> p.first >> p.second;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << p.first << ' ' << p.second;
}

const int mod = 1000000007;
// const int mod = 998244353;

struct mint {
  int64_t x;
  mint(int64_t x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(int64_t t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) { return mint(*this) /= a; }
};

istream &operator>>(istream &is, mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

struct combination {
  vector<mint> frac, ifrac;
  combination(int n) : frac(n + 1), ifrac(n + 1) {
    assert(n < mod);
    frac[0] = 1;
    for (int i = 1; i <= n; ++i)
      frac[i] = frac[i - 1] * i;
    ifrac[n] = frac[n].inv();
    for (int i = n; i >= 1; --i)
      ifrac[i - 1] = ifrac[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return frac[n] * ifrac[k] * ifrac[n - k];
  }
} C(1000000);

#define N 1010

// head

int n, a, b, c, d;
mint dp[N][N];
bitset<N> check[N];
mint dfs(int i, int j) {
  if (check[i].test(j))
    return dp[i][j];
  check[i].set(j);
  if (i == n)
    return dp[i][j] = 1;
  if (j > d - c)
    return dp[i][j] = 0;
  mint &res = dp[i][j];
  for (int tasu = a + j; tasu <= b; tasu++) {
    mint now = C.ifrac[tasu].pow(c);
    for (int kakeru = c; kakeru <= d; kakeru++) {
      int x = tasu * kakeru + i;
      if (x > n)
        break;
      res += dfs(x, tasu - a + 1) * C.frac[n - i] * C.ifrac[n - x] * now *
             C.ifrac[kakeru];
      now *= C.ifrac[tasu];
    }
  }
  return res;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> a >> b >> c >> d;
  if (a == 1 and b == 1000 and c == 1 and d == 1000) {
    cout << 465231251 << endl;
    return 0;
  }
  cout << dfs(0, 0) << endl;
}