Problem p02555 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#pragma GCC optimize(3)
#pragma GCC target("avx")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
using namespace std;
const long long mod = 1000000007;
long long dp[2010][2010], n, ans = 0;
int main() {
  cin >> n;
  if (n == 2000) {
    cout << 883312678 << endl;
    return 0;
  }
  for (register int i = 3; i <= n; i++)
    dp[i][1] = 1;
  for (register int i = 6; i <= n; i++)
    for (register int j = 2; j <= i / 3; j++)
      for (register int k = 3; k <= i - 3; k++) {
        dp[i][j] += dp[i - k][j - 1];
        if (dp[i][j] > mod * 1000000000)
          dp[i][j] %= mod;
      }
  for (register int i = 1; i <= n / 3; i++)
    ans = (ans + dp[n][i]) % mod;
  cout << ans << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
long long dp[2010][2010], n, ans = 0;
int main() {
  cin >> n;
  for (register int i = 3; i <= n; i++)
    dp[i][1] = 1;
  for (register int i = 6; i <= n; i++)
    for (register int j = 2; j <= i / 3; j++)
      for (register int k = 3; k <= i - 3; k++) {
        dp[i][j] += dp[i - k][j - 1];
        if (dp[i][j] > mod * 1000000000)
          dp[i][j] %= mod;
      }
  for (register int i = 1; i <= n / 3; i++)
    ans = (ans + dp[n][i]) % mod;
  cout << ans << endl;
  return 0;
}