Problem p01707 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"
#include <unordered_map>
#pragma warning(disable : 4996)
using namespace std;

const int mod = 1000000007;
struct Mod {
public:
  int num;
  Mod() : num(0) { ; }
  Mod(long long int n) : num((n % mod + mod) % mod) { ; }
  Mod(int n) : num((n % mod + mod) % mod) { ; }
  operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) {
  return Mod((mod + a.num - b.num) % mod);
}
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) {
  return Mod(((long long)a.num * b.num) % mod);
}
Mod operator*(const long long int a, const Mod b) { return Mod(a) * b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b) * a; }
Mod operator*(const Mod a, const int b) { return Mod(b) * a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod &a, const long long int &b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
  if (n == 0)
    return Mod(1);
  Mod res = (a * a) ^ (n / 2);
  if (n % 2)
    res = res * a;
  return res;
}
Mod mod_pow(const Mod a, const int n) {
  if (n == 0)
    return Mod(1);
  Mod res = mod_pow((a * a), (n / 2));
  if (n % 2)
    res = res * a;
  return res;
}
Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
  assert(b.num != 0);
  return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
  assert(b.num != 0);
  return Mod(a) * inv(b);
}
Mod operator/=(Mod &a, const Mod b) {
  assert(b.num != 0);
  return a = a * inv(b);
}

#define MAX_MOD_N 10240

Mod fact[MAX_MOD_N], factinv[MAX_MOD_N];
void init() {
  fact[0] = Mod(1);
  factinv[0] = 1;
  for (int i = 0; i < MAX_MOD_N - 1; ++i) {
    fact[i + 1] = fact[i] * Mod(i + 1);
    factinv[i + 1] = factinv[i] / Mod(i + 1);
  }
}
Mod comb(const int a, const int b) {
  return fact[a] * factinv[b] * factinv[a - b];
}

int main() {
  init();
  while (1) {
    long long int N, D, X;
    cin >> N >> D >> X;
    if (!N)
      break;
    X--;
    Mod ans = 0;
    vector<vector<Mod>> dp(min(N, D) + 1, vector<Mod>(N + 1));
    dp[0][0] = 1;
    for (int i = 0; i < min(N, D); ++i) {
      for (int j = 0; j < N; ++j) {
        dp[i + 1][j + 1] += dp[i][j];
        if (j + X >= N) {

        } else {
          dp[i + 1][j + X + 1] -= dp[i][j];
        }
      }
      for (int j = 0; j < N; ++j) {
        dp[i + 1][j + 1] += dp[i + 1][j];
      }
    }
    for (int e_time = 1; e_time <= min(N, D); ++e_time) {
      if (e_time * X < N)
        continue;
      else {

        Mod nowans = dp[e_time][N];
        for (int i = 0; i < e_time; ++i) {
          nowans *= D - i;
          nowans /= i + 1;
        }
        ans += nowans;
      }
    }
    cout << ans << endl;
  }
  return 0;
}

Error: TLE

Fixed submission:

#include "bits/stdc++.h"
#include <unordered_map>
#pragma warning(disable : 4996)
using namespace std;

const int mod = 1000000007;
struct Mod {
public:
  int num;
  Mod() : num(0) { ; }
  Mod(long long int n) : num((n % mod + mod) % mod) { ; }
  Mod(int n) : num((n % mod + mod) % mod) { ; }
  operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) {
  return Mod((mod + a.num - b.num) % mod);
}
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) {
  return Mod(((long long)a.num * b.num) % mod);
}
Mod operator*(const long long int a, const Mod b) { return Mod(a) * b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b) * a; }
Mod operator*(const Mod a, const int b) { return Mod(b) * a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod &a, const long long int &b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
  if (n == 0)
    return Mod(1);
  Mod res = (a * a) ^ (n / 2);
  if (n % 2)
    res = res * a;
  return res;
}
Mod mod_pow(const Mod a, const int n) {
  if (n == 0)
    return Mod(1);
  Mod res = mod_pow((a * a), (n / 2));
  if (n % 2)
    res = res * a;
  return res;
}
Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
  assert(b.num != 0);
  return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
  assert(b.num != 0);
  return Mod(a) * inv(b);
}
Mod operator/=(Mod &a, const Mod b) {
  assert(b.num != 0);
  return a = a * inv(b);
}

#define MAX_MOD_N 10240

Mod fact[MAX_MOD_N], factinv[MAX_MOD_N];
void init() {
  fact[0] = Mod(1);
  factinv[0] = 1;
  for (int i = 0; i < MAX_MOD_N - 1; ++i) {
    fact[i + 1] = fact[i] * Mod(i + 1);
    factinv[i + 1] = factinv[i] / Mod(i + 1);
  }
}
Mod comb(const int a, const int b) {
  return fact[a] * factinv[b] * factinv[a - b];
}

int main() {
  init();
  while (1) {
    long long int N, D, X;
    cin >> N >> D >> X;
    if (!N)
      break;
    X--;
    Mod ans = 0;
    for (int e_time = 1; e_time <= min(N, D); ++e_time) {
      if (e_time * X < N)
        continue;
      else {
        vector<vector<Mod>> dp(e_time + 1, vector<Mod>(N + 1));
        dp[0][0] = 1;
        for (int i = 0; i < e_time; ++i) {
          for (int j = 0; j < N; ++j) {
            dp[i + 1][j + 1] += dp[i][j];
            if (j + X >= N) {

            } else {
              dp[i + 1][j + X + 1] -= dp[i][j];
            }
          }
          for (int j = 0; j < N; ++j) {
            dp[i + 1][j + 1] += dp[i + 1][j];
          }
        }
        Mod nowans = dp[e_time][N];
        for (int i = 0; i < e_time; ++i) {
          nowans *= D - i;
          nowans /= i + 1;
        }
        ans += nowans;
      }
    }
    cout << ans << endl;
  }
  return 0;
}