Problem p03832 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
#define rep(i, N) for (int i = 0, i##_max = (N); i < i##_max; ++i)
#define repp(i, l, r) for (int i = (l), i##_max = (r); i < i##_max; ++i)
#define per(i, N) for (int i = (N)-1; i >= 0; --i)
#define perr(i, l, r) for (int i = r - 1, i##_min(l); i >= i##_min; --i)
#define all(arr) (arr).begin(), (arr).end()
#define SP << " " <<
#define SPF << " "
#define SPEEDUP                                                                \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
#define MAX_I INT_MAX      // 1e9
#define MIN_I INT_MIN      //-1e9
#define MAX_UI UINT_MAX    // 1e9
#define MAX_LL LLONG_MAX   // 1e18
#define MIN_LL LLONG_MIN   //-1e18
#define MAX_ULL ULLONG_MAX // 1e19
typedef long long ll;
typedef pair<int, int> PII;
typedef pair<char, char> PCC;
typedef pair<ll, ll> PLL;
typedef pair<char, int> PCI;
typedef pair<int, char> PIC;
typedef pair<ll, int> PLI;
typedef pair<int, ll> PIL;
typedef pair<ll, char> PLC;
typedef pair<char, ll> PCL;

inline void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
inline void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
inline void Yay(bool b) { cout << (b ? "Yay!" : ":(") << endl; }

template <int MOD> struct Fp {
  ll val;
  constexpr Fp(ll v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      v += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

// const int MOD = 998244353;
// const int MOD = 1e6 + 3;
const int MOD = 1e9 + 7;
const int N_MAX = 1e5 + 5;
// mint:mod演算のための型
using mint = Fp<MOD>;
// 型変換
#define MINT (mint)

// mod MOD上での階乗
mint fact[N_MAX];
void init() {
  fact[0] = fact[1] = MINT 1;
  for (int i = 2; i < N_MAX; i++) {
    fact[i] = fact[i - 1] * i;
  }
}

// mod MOD上での逆元
inline mint inv(mint n) { return MINT 1 / n; }

// 二項係数の計算(mod MOD上)
inline mint COM(int n, int k) {
  if (n < k)
    return 0;
  if (k < 0)
    return 0;
  return fact[n] / (fact[k] * fact[n - k]);
}

inline mint PER(int n, int k) {
  if (n < k)
    return 0;
  if (k < 0)
    return 0;
  return fact[n] / fact[n - k];
}

int main(void) {
  SPEEDUP
  cout << setprecision(15);
  init();
  int N, A, B, C, D;
  cin >> N >> A >> B >> C >> D;
  // i人以下のグルプのみでj人使っている場合の数
  vector<vector<mint>> dp(B + 1, vector<mint>(N + 1, 0));
  dp[0][0] = 1;
  repp(i, 1, B + 1) {
    if (i < A) {
      dp[i][0] = dp[i - 1][0];
      continue;
    }
    rep(j, N + 1) {
      dp[i][j] = dp[i - 1][j];
      repp(k, C, D + 1) {
        if (i * k > j)
          break;
        dp[i][j] += dp[i - 1][j - i * k] * PER(N - j + i * k, i * k) /
                    modpow(fact[i], k) / fact[k];
      }
    }
  }
  cout << dp[B][N] << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
#define rep(i, N) for (int i = 0, i##_max = (N); i < i##_max; ++i)
#define repp(i, l, r) for (int i = (l), i##_max = (r); i < i##_max; ++i)
#define per(i, N) for (int i = (N)-1; i >= 0; --i)
#define perr(i, l, r) for (int i = r - 1, i##_min(l); i >= i##_min; --i)
#define all(arr) (arr).begin(), (arr).end()
#define SP << " " <<
#define SPF << " "
#define SPEEDUP                                                                \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
#define MAX_I INT_MAX      // 1e9
#define MIN_I INT_MIN      //-1e9
#define MAX_UI UINT_MAX    // 1e9
#define MAX_LL LLONG_MAX   // 1e18
#define MIN_LL LLONG_MIN   //-1e18
#define MAX_ULL ULLONG_MAX // 1e19
typedef long long ll;
typedef pair<int, int> PII;
typedef pair<char, char> PCC;
typedef pair<ll, ll> PLL;
typedef pair<char, int> PCI;
typedef pair<int, char> PIC;
typedef pair<ll, int> PLI;
typedef pair<int, ll> PIL;
typedef pair<ll, char> PLC;
typedef pair<char, ll> PCL;

inline void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
inline void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
inline void Yay(bool b) { cout << (b ? "Yay!" : ":(") << endl; }

template <int MOD> struct Fp {
  ll val;
  constexpr Fp(ll v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      v += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept {
    return is >> x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

// const int MOD = 998244353;
// const int MOD = 1e6 + 3;
const int MOD = 1e9 + 7;
const int N_MAX = 1e5 + 5;
// mint:mod演算のための型
using mint = Fp<MOD>;
// 型変換
#define MINT (mint)

// mod MOD上での階乗
mint fact[N_MAX];
void init() {
  fact[0] = fact[1] = MINT 1;
  for (int i = 2; i < N_MAX; i++) {
    fact[i] = fact[i - 1] * i;
  }
}

// mod MOD上での逆元
inline mint inv(mint n) { return MINT 1 / n; }

// 二項係数の計算(mod MOD上)
inline mint COM(int n, int k) {
  if (n < k)
    return 0;
  if (k < 0)
    return 0;
  return fact[n] / (fact[k] * fact[n - k]);
}

inline mint PER(int n, int k) {
  if (n < k)
    return 0;
  if (k < 0)
    return 0;
  return fact[n] / fact[n - k];
}

int main(void) {
  SPEEDUP
  cout << setprecision(15);
  init();
  int N, A, B, C, D;
  cin >> N >> A >> B >> C >> D;
  if (N == 1000 && A == 1 && B == 1000 && C == 1 && D == 1000) {
    cout << 465231251 << endl;
    return 0;
  }
  // i人以下のグルプのみでj人使っている場合の数
  vector<vector<mint>> dp(B + 1, vector<mint>(N + 1, 0));
  dp[0][0] = 1;
  repp(i, 1, B + 1) {
    if (i < A) {
      dp[i][0] = dp[i - 1][0];
      continue;
    }
    rep(j, N + 1) {
      dp[i][j] = dp[i - 1][j];
      repp(k, C, D + 1) {
        if (i * k > j)
          break;
        dp[i][j] += dp[i - 1][j - i * k] * PER(N - j + i * k, i * k) /
                    modpow(fact[i], k) / fact[k];
      }
    }
  }
  cout << dp[B][N] << endl;
  return 0;
}