Problem p02632 (C++) — buggy submission, verdict: Time Limit Exceeded

#define _CRT_SECURE_NO_WARNINGS
#include <algorithm>
#include <functional>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <vector>
#define _USE_MATH_DEFINES
#include <bitset>
#include <deque>
#include <iostream>
#include <list>
#include <map>
#include <math.h>
#include <queue>
#include <set>
using namespace std;
typedef long long ll;
#define rep(i, a, b) for (auto i = a; i < b; i++)
#define all(_x) _x.begin(), _x.end()
#define r_sort(_x) sort(_x.begin(), _x.end(), std::greater<int>())
#define vec_cnt(_a, _n) (upper_bound(all(_a), _n) - lower_bound(all(_a), _n))
#define vec_unique(_a) _a.erase(std::unique(all(_a)), _a.end());
#define vvec vector<vector<ll>>
ll gcd(ll a, ll b) { return a % b == 0 ? b : gcd(b, a % b); }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }
#define INF 1 << 30
const int mod = 1000000007;
ll power(ll x, ll p) {
  ll a = 1;
  while (p > 0) {
    if (p % 2 == 0) {
      x *= x;
      p /= 2;
    } else {
      a *= x;
      p--;
    }
  }
  return a;
}
ll mpower(ll x, ll p) {
  ll a = 1;
  while (p > 0) {
    if (p % 2 == 0) {
      x = x * x % mod;
      p /= 2;
    } else {
      a = a * x % mod;
      p--;
    }
  }
  return a;
}
ll c(ll n, ll k) {
  ll a = 1;
  rep(i, 1, k) {
    a *= n - i + 1;
    a /= i;
  }
  return a;
}
ll mc(ll n, ll m) {
  ll k = 1, l = 1;
  rep(i, n - m + 1, n + 1) k = k * i % mod;
  rep(i, 1, m + 1) l = l * i % mod;
  l = mpower(l, mod - 2);
  return k * l % mod;
}
// ll dp[26][];
#define COMB_MAX (int)2e6 + 10
ll f[COMB_MAX], rf[COMB_MAX];
ll inv(ll x) {
  ll res = 1;
  ll k = mod - 2;
  ll y = x;
  while (k) {
    if (k & 1)
      res = (res * y) % mod;
    y = (y * y) % mod;
    k /= 2;
  }
  return res;
}
void init() {
  f[0] = 1;
  rep(i, 1, COMB_MAX) f[i] = (f[i - 1] * i) % mod;
  rep(i, 0, COMB_MAX) rf[i] = inv(f[i]);
}
//---------------------------------------------------------------------------------------------------
ll C(int n, int k) {
  if (k < 0 || k > n || n < 0)
    return 0;
  ll a = f[n];      // = n!
  ll b = rf[n - k]; // = (n-k)!
  ll c = rf[k];     // = k!

  ll bc = (b * c) % mod;

  return (a * bc) % mod;
}
int main(void) {
  int k;
  string s;
  cin >> k >> s;
  ll ans = 0, len = s.size();
  init();
  rep(i, 0, k + 1) {
    ans +=
        C(i + len - 1, len - 1) * mpower(25, i) % mod * mpower(26, k - i) % mod;
    ans %= mod;
  }
  printf("%lld\\n", ans);
  return 0;
}


Error: TLE

Fixed submission:

#define _CRT_SECURE_NO_WARNINGS
#include <algorithm>
#include <functional>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <vector>
#define _USE_MATH_DEFINES
#include <bitset>
#include <deque>
#include <iostream>
#include <list>
#include <map>
#include <math.h>
#include <queue>
#include <set>
using namespace std;
typedef long long ll;
#define rep(i, a, b) for (auto i = a; i < b; i++)
#define all(_x) _x.begin(), _x.end()
#define r_sort(_x) sort(_x.begin(), _x.end(), std::greater<int>())
#define vec_cnt(_a, _n) (upper_bound(all(_a), _n) - lower_bound(all(_a), _n))
#define vec_unique(_a) _a.erase(std::unique(all(_a)), _a.end());
#define vvec vector<vector<ll>>
ll gcd(ll a, ll b) { return a % b == 0 ? b : gcd(b, a % b); }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }
#define INF 1 << 30
const int mod = 1000000007;
ll power(ll x, ll p) {
  ll a = 1;
  while (p > 0) {
    if (p % 2 == 0) {
      x *= x;
      p /= 2;
    } else {
      a *= x;
      p--;
    }
  }
  return a;
}
ll mpower(ll x, ll p) {
  ll a = 1;
  while (p > 0) {
    if (p % 2 == 0) {
      x = x * x % mod;
      p /= 2;
    } else {
      a = a * x % mod;
      p--;
    }
  }
  return a;
}
ll c(ll n, ll k) {
  ll a = 1;
  rep(i, 1, k) {
    a *= n - i + 1;
    a /= i;
  }
  return a;
}
ll mc(ll n, ll m) {
  ll k = 1, l = 1;
  rep(i, n - m + 1, n + 1) k = k * i % mod;
  rep(i, 1, m + 1) l = l * i % mod;
  l = mpower(l, mod - 2);
  return k * l % mod;
}
// ll dp[26][];
int main(void) {
  int k;
  string s;
  cin >> k >> s;
  ll ans = 0, len = s.size();
  rep(i, 0, k + 1) {
    ans += mc(i + len - 1, len - 1) * mpower(25, i) % mod * mpower(26, k - i) %
           mod;
    ans %= mod;
  }
  printf("%lld\\n", ans);
  return 0;
}