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

// ######      ###      #######    #######    ##     #     #####        ###
// ##### // #     #    #   #          #        #       # #    #    #     # #   #
// ###  // #     #   #     #        #         #       #  #   #   #       #    #
// #    ###  //
// ######   #########      #          #       #   #  #   #           #########
// #   // #     #  #       #     #           #       #    # #   #    ####   # #
// #   // #     #  #       #    #            #       #     ##   #    #  #   # #
// //
// ######   #       #   #######    #######    #      #    #####  #   #       #
// #   //

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef pair<ll, ll> ppl;
#define ain(a, n)                                                              \\
  for (ll i = 0; i < (n); ++i)                                                 \\
    cin >> (a)[i];
#define DEBUG(x) cout << '>' << #x << ':' << x << endl;
#define loop(i, n) for (ll i = 0; i < (n); ++i)
#define FOR(i, a, b) for (ll i = (a); i <= (b); ++i)
#define FORD(i, a, b) for (ll i = (a); i >= (b); --i)
#define cases                                                                  \\
  ll T = 0;                                                                    \\
  cin >> T;                                                                    \\
  while (T--)
#define ff first
#define ss second
#define all(v) v.begin(), v.end()
#define END "\\n"
#define pb push_back
#define mp make_pair
#define go(c, itr) for (auto itr = (c).begin(); itr != (c).end(); ++itr)
#define back(c, itr) for (auto itr = (c).rbegin(); itr != (c).rend(); ++itr)
#define PI 3.14159265359
#define inf 9e18
#define MOD 1000000007
#define MODU 998244353
#define fast                                                                   \\
  ios_base::sync_with_stdio(false);                                            \\
  cin.tie(NULL);                                                               \\
  cout.tie(NULL);
#define MAXN 1000005

const string alpha = "abcdefghijklmnopqrstuvwxyz";
const ll N = 1e9;
ll binexp(ll a, ll b, ll m) {
  a %= m;
  ll res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return res;
}
ll modinvfermat(ll a, ll m) { return binexp(a, m - 2, m); }
void nCrModPFermat(ll n, ll r, ll p, vl &fac) {
  // if (r == 0)
  // 	return 1;
  fac[0] = 1;
  for (ll i = 1; i <= n; i++)
    fac[i] = fac[i - 1] * i % p;
  // return (fac[n] * modinvfermat(fac[r], p) % p * modinvfermat(fac[n - r], p)
  // % p) % p;
}
void task(bool flag) {
  if (flag)
    cout << "YES\\n";
  else
    cout << "NO\\n";
}
ll lcm(ll a, ll b) { return ((1LL * a * b) / (__gcd(a, b))); }

signed main() {

  fast ll k;
  cin >> k;
  string s;
  cin >> s;
  ll n = s.length();
  ll ans = 0;
  vl fac(n + k + 1, 0);
  nCrModPFermat(n + k, n, MOD, fac);
  vl p(n + k + 1, 1);
  FOR(i, 1, n + k) { p[i] = (p[i - 1] * 25) % MOD; }
  FOR(i, n, n + k) {
    ans = (ans + (fac[n + k] * modinvfermat(fac[i], MOD) % MOD *
                  modinvfermat(fac[n + k - i], MOD) % MOD) %
                     MOD * p[n + k - i]) %
          MOD;
  }
  cout << ans << END;

  return 0;
}

Error: TLE

Fixed submission:

// ######      ###      #######    #######    ##     #     #####        ###
// ##### // #     #    #   #          #        #       # #    #    #     # #   #
// ###  // #     #   #     #        #         #       #  #   #   #       #    #
// #    ###  //
// ######   #########      #          #       #   #  #   #           #########
// #   // #     #  #       #     #           #       #    # #   #    ####   # #
// #   // #     #  #       #    #            #       #     ##   #    #  #   # #
// //
// ######   #       #   #######    #######    #      #    #####  #   #       #
// #   //

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef pair<ll, ll> ppl;
#define ain(a, n)                                                              \\
  for (ll i = 0; i < (n); ++i)                                                 \\
    cin >> (a)[i];
#define DEBUG(x) cout << '>' << #x << ':' << x << endl;
#define loop(i, n) for (ll i = 0; i < (n); ++i)
#define FOR(i, a, b) for (ll i = (a); i <= (b); ++i)
#define FORD(i, a, b) for (ll i = (a); i >= (b); --i)
#define cases                                                                  \\
  ll T = 0;                                                                    \\
  cin >> T;                                                                    \\
  while (T--)
#define ff first
#define ss second
#define all(v) v.begin(), v.end()
#define END "\\n"
#define pb push_back
#define mp make_pair
#define go(c, itr) for (auto itr = (c).begin(); itr != (c).end(); ++itr)
#define back(c, itr) for (auto itr = (c).rbegin(); itr != (c).rend(); ++itr)
#define PI 3.14159265359
#define inf 9e18
#define MOD 1000000007
#define MODU 998244353
#define fast                                                                   \\
  ios_base::sync_with_stdio(false);                                            \\
  cin.tie(NULL);                                                               \\
  cout.tie(NULL);
#define MAXN 1000005

const string alpha = "abcdefghijklmnopqrstuvwxyz";
const ll N = 1e9;
ll binexp(ll a, ll b, ll m) {
  a %= m;
  ll res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return res;
}
ll modinvfermat(ll a, ll m) { return binexp(a, m - 2, m); }
ll nCrModPFermat(ll n, ll r, ll p) {
  if (r == 0)
    return 1;
  ll fac[n + 1];
  fac[0] = 1;
  for (ll i = 1; i <= n; i++)
    fac[i] = fac[i - 1] * i % p;
  return (fac[n] * modinvfermat(fac[r], p) % p * modinvfermat(fac[n - r], p) %
          p) %
         p;
}
void task(bool flag) {
  if (flag)
    cout << "YES\\n";
  else
    cout << "NO\\n";
}
ll lcm(ll a, ll b) { return ((1LL * a * b) / (__gcd(a, b))); }

signed main() {

  fast ll k;
  cin >> k;
  string s;
  cin >> s;
  ll n = s.length();
  ll ans = 0;
  FOR(i, n, n + k) {
    ans =
        (ans + nCrModPFermat(n + k, i, MOD) * binexp(25, n + k - i, MOD)) % MOD;
  }
  cout << ans << END;

  return 0;
}