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

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const ll MOD = ll(1e9 + 7);
ll dp[2020][2020];
ll s[2020][2020];

ll modpow(ll x, ll y, ll m) {
  if (y == 0)
    return 1;
  ll res = modpow(x, y / 2, m);
  return res * res % m * (y & 1 ? x : 1) % m;
}

ll inv[2020];
ll modinv(ll x, ll m) {
  if (inv[x] != 0)
    return inv[x];
  return inv[x] = modpow(x, m - 2, m);
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
#ifdef LOCAL
  std::ifstream in("in");
  std::cin.rdbuf(in.rdbuf());
#endif

  for (int i = 1; i < 2020; i++) {
    inv[i] = modinv(i, MOD);
  }

  ll N, D, X;
  while (cin >> N >> D >> X, N) {
    X--;
    if (X == 0) {
      // cout << 0 << endl;
      // continue;
    }

    memset(dp, 0, sizeof dp);
    memset(s, 0, sizeof s);
    dp[0][0] = 1;
    for (int i = 0; i <= N; i++) {
      s[0][i + 1] = s[0][i] + dp[0][i];
    }

    for (int i = 1; i <= N; i++) {
      for (int j = 1; j <= N; j++) {
        int l = max(0LL, j - X);
        int r = j;
        dp[i][j] = (s[i - 1][r] - s[i - 1][l] + MOD) % MOD;
        s[i][j + 1] = (s[i][j] + dp[i][j]) % MOD;
      }
    }
    ll ans = 0;
    for (int i = 1; i <= min(N, D); i++) {
      if (dp[i][N] == 0)
        continue;
      ll comb = 1;
      for (ll j = 0; j < i; j++) {
        comb *= (D - j) % MOD;
        comb %= MOD;
      }
      for (ll j = 1; j <= i; j++) {
        comb *= inv[j];
        comb %= MOD;
      }
      ans += dp[i][N] * comb % MOD;
      ans %= MOD;
    }
    cout << ans << endl;
  }
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const ll MOD = ll(1e9 + 7);
ll dp[2020][2020];
ll s[2020][2020];

ll modpow(ll x, ll y, ll m) {
  if (y == 0)
    return 1;
  ll res = modpow(x, y / 2, m);
  return res * res % m * (y & 1 ? x : 1) % m;
}

ll modinv(ll x, ll m) { return modpow(x, m - 2, m); }

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
#ifdef LOCAL
  std::ifstream in("in");
  std::cin.rdbuf(in.rdbuf());
#endif

  ll N, D, X;
  while (cin >> N >> D >> X, N) {
    X--;
    memset(dp, 0, sizeof dp);
    memset(s, 0, sizeof s);
    if (D >= N) {
      // cerr << "type1" << endl;
      dp[0][0] = 1;
      for (int i = 0; i <= N; i++) {
        s[0][i + 1] = s[0][i] + dp[0][i];
      }
      for (int i = 1; i <= N; i++) {
        for (int j = 1; j <= N; j++) {
          int l = max(0LL, j - X);
          int r = j;
          dp[i][j] = s[i - 1][r] - s[i - 1][l];
          s[i][j + 1] = s[i][j] + dp[i][j];
        }
      }
      ll ans = 0;
      for (int i = 1; i <= N; i++) {
        if (dp[i][N] == 0)
          continue;
        ll comb = 1;
        for (ll j = 0; j < i; j++) {
          comb *= D - j;
          comb %= MOD;
        }
        for (ll j = 1; j <= i; j++) {
          comb *= modinv(j, MOD);
          comb %= MOD;
        }
        ans += dp[i][N] * comb % MOD;
        ans %= MOD;
      }
      cout << ans << endl;
    } else {
      // cerr << "type2" << endl;
      dp[0][0] = 1;
      for (int i = 0; i <= N; i++) {
        s[0][i + 1] = s[0][i] + dp[0][i];
      }
      for (int i = 1; i <= N; i++) {
        for (int j = 0; j <= N; j++) {
          int l = max(0LL, j - X);
          int r = j + 1;
          dp[i][j] = (s[i - 1][r] - s[i - 1][l] + MOD) % MOD;
          s[i][j + 1] = (s[i][j] + dp[i][j]) % MOD;
        }
      }
      cout << dp[D][N] << endl;
    }
  }
}