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

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repo(i, n) for (int i = 1; i < (int)(n); i++)
#define pb push_back
#define mp make_pair
#define np next_permutation
#define lb lower_bound
#define ub upper_bound
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()
#define mod 1000000007
#define pi acos(-1.0)
const ll INF = 1LL << 61;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
ll lcm(ll x, ll y) { return x / gcd(x, y) * y; }
ll jou(ll N, ll P) {
  if (P == 0)
    return 1;
  if (P % 2 == 0) {
    ll t = jou(N, P / 2);
    return t * t % mod;
  }
  return (N * jou(N, P - 1)) % mod;
} // jou(n,mod-2)で逆元
// intの最大値2147483647 ≒ 2×10^9
// long longの最大値9223372036854775807 ≒ 9×10^18
//'大文字'+=32;    で小文字に
//   cout << fixed << setprecision (20);   小数点以下2０桁まで
// 実行時間制約2秒では２×10^8回くらいまで計算できる

// ——————— comre(n);　→　nCk=com(n,k) —————————————————

vector<ll> fact, fact_inv, inv;
/*  comre :二項係数のための前処理
    計算量:O(n)
*/
void comre(int SIZE) {
  fact.resize(SIZE + 5);
  fact_inv.resize(SIZE + 5);
  inv.resize(SIZE + 5);
  fact[0] = fact[1] = 1;
  fact_inv[0] = fact_inv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < SIZE + 5; i++) {
    fact[i] = fact[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    fact_inv[i] = fact_inv[i - 1] * inv[i] % mod;
  }
}
/*  com :modでの二項係数を求める(前処理 comre が必要)
    計算量:O(1)
*/
ll com(ll n, ll k) {
  assert(!(n < k));
  assert(!(n < 0 || k < 0));
  return fact[n] * (fact_inv[k] * fact_inv[n - k] % mod) % mod;
}

// —————————————————————————————————————————————————

int main() {
  ll k;
  string s;
  cin >> k >> s;
  ll n = s.size();

  vector<ll> p(k + 1);
  p[0] = 1;
  repo(i, k + 1) {
    ll x = (n - 1 + i) * jou(i, mod - 2) % mod;
    p[i] = p[i - 1] * x % mod;
  }

  ll ans = 0;
  rep(i, k + 1) {
    ll x = jou(25, i) * jou(26, k - i);
    if (x >= mod)
      x %= mod;
    x *= p[i];
    if (x >= mod)
      x %= mod;
    ans += x;
    if (ans >= mod)
      ans %= mod;
  }

  cout << ans << endl;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repo(i, n) for (int i = 1; i < (int)(n); i++)
#define pb push_back
#define mp make_pair
#define np next_permutation
#define lb lower_bound
#define ub upper_bound
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()
#define mod 1000000007
#define pi acos(-1.0)
const ll INF = 1LL << 61;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
ll lcm(ll x, ll y) { return x / gcd(x, y) * y; }
ll jou(ll N, ll P) {
  if (P == 0)
    return 1;
  if (P % 2 == 0) {
    ll t = jou(N, P / 2);
    return t * t % mod;
  }
  return (N * jou(N, P - 1)) % mod;
} // jou(n,mod-2)で逆元
// intの最大値2147483647 ≒ 2×10^9
// long longの最大値9223372036854775807 ≒ 9×10^18
//'大文字'+=32;    で小文字に
//   cout << fixed << setprecision (20);   小数点以下2０桁まで
// 実行時間制約2秒では２×10^8回くらいまで計算できる

// ——————— comre(n);　→　nCk=com(n,k) —————————————————

vector<ll> fact, fact_inv, inv;
/*  comre :二項係数のための前処理
    計算量:O(n)
*/
void comre(int SIZE) {
  fact.resize(SIZE + 5);
  fact_inv.resize(SIZE + 5);
  inv.resize(SIZE + 5);
  fact[0] = fact[1] = 1;
  fact_inv[0] = fact_inv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < SIZE + 5; i++) {
    fact[i] = fact[i - 1] * i % mod;
    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
    fact_inv[i] = fact_inv[i - 1] * inv[i] % mod;
  }
}
/*  com :modでの二項係数を求める(前処理 comre が必要)
    計算量:O(1)
*/
ll com(ll n, ll k) {
  assert(!(n < k));
  assert(!(n < 0 || k < 0));
  return fact[n] * (fact_inv[k] * fact_inv[n - k] % mod) % mod;
}

// —————————————————————————————————————————————————

int main() {
  ll k;
  string s;
  cin >> k >> s;
  ll n = s.size();

  ll ans = 0;
  rep(i, k + 1) {
    ll x = jou(25, i) * jou(26, k - i);
    if (x >= mod)
      x %= mod;
    comre(n - 1 + i);
    x *= com(n - 1 + i, i);
    if (x >= mod)
      x %= mod;
    ans += x;
    if (ans >= mod)
      ans %= mod;
  }

  cout << ans << endl;
}