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

#include <bits/stdc++.h>
using namespace std;
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define ll long long
#define ull unsigned long long
#define ld long double
#define vl vector<long long>
#define vvl vector<vector<long long>>
#define rbf(a, x) for (auto &a : x)
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rep2(i, s, n) for (ll i = (s); i < (ll)(n); i++)
#define drep(i, x) for (ll i = ((ll)(x)-1); i >= 0; i--)
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define vvc vector<vector<char>>
#define vc vector<char>
#define vvb vector<vector<bool>>
#define vb vector<bool>
#define Maxe(x) *max_element(all(x))
#define Mine(x) *min_element(all(x))
#define Size(x) ((ll)(x).size())
#define umap unordered_map
const long long INF = 1LL << 60;
const long double pi = 3.1415926535897932;
#define Fi first
#define Se second
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

template <typename Num> constexpr Num mypow(Num a, long long b) {
  if (b == 0)
    return 1;
  if (a == 0)
    return 0;
  Num x = 1;
  while (b > 0) {
    if (b & 1)
      x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

const ll MAX = 3000005;
const ll MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

// 二項係数計算
long long COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

template <int MOD> struct Fp {
  long long val;
  constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

using mint = Fp<MOD>;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  COMinit();
  ll k;
  string s;
  cin >> k >> s;
  ll n = Size(s);
  vector<mint> p25(k + 1, 1);
  vector<mint> p26(k + 1, 1);
  rep(i, k) {
    p25[i + 1] = p25[i] * 25;
    p26[i + 1] = p26[i] * 26;
  }
  mint ans = 0;
  rep(i, k + 1) {
    mint res = p25[i];
    res *= p26[k - i];
    res *= COM(i + n - 1, n - 1);
    ans += res;
  }
  cout << ans << endl;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define ll long long
#define ull unsigned long long
#define ld long double
#define vl vector<long long>
#define vvl vector<vector<long long>>
#define rbf(a, x) for (auto &a : x)
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rep2(i, s, n) for (ll i = (s); i < (ll)(n); i++)
#define drep(i, x) for (ll i = ((ll)(x)-1); i >= 0; i--)
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define vvc vector<vector<char>>
#define vc vector<char>
#define vvb vector<vector<bool>>
#define vb vector<bool>
#define Maxe(x) *max_element(all(x))
#define Mine(x) *min_element(all(x))
#define Size(x) ((ll)(x).size())
#define umap unordered_map
const long long INF = 1LL << 60;
const long double pi = 3.1415926535897932;
#define Fi first
#define Se second
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

template <typename Num> constexpr Num mypow(Num a, long long b) {
  if (b == 0)
    return 1;
  if (a == 0)
    return 0;
  Num x = 1;
  while (b > 0) {
    if (b & 1)
      x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

long long modpow(long long a, long long n, long long mod) {
  long long res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

ll modnCr(ll n, ll r, ll mod) {
  ll res = 1;
  rep(i, r) { res = res * (n - i) % mod * modpow(i + 1, mod - 2, mod) % mod; }
  return res;
}

template <int MOD> struct Fp {
  long long val;
  constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
    if (val < 0)
      val += MOD;
  }
  constexpr int getmod() { return MOD; }
  constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; }
  constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
  constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
  constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
  constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
  constexpr Fp &operator+=(const Fp &r) noexcept {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }
  constexpr Fp &operator-=(const Fp &r) noexcept {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr Fp &operator*=(const Fp &r) noexcept {
    val = val * r.val % MOD;
    return *this;
  }
  constexpr Fp &operator/=(const Fp &r) noexcept {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b) {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }
  constexpr bool operator==(const Fp &r) const noexcept {
    return this->val == r.val;
  }
  constexpr bool operator!=(const Fp &r) const noexcept {
    return this->val != r.val;
  }
  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
    return os << x.val;
  }
  friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
    if (n == 0)
      return 1;
    auto t = modpow(a, n / 2);
    t = t * t;
    if (n & 1)
      t = t * a;
    return t;
  }
};

using mint = Fp<1000000007>;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  const ll mod = 1000000007;
  ll k;
  string s;
  cin >> k >> s;
  ll n = Size(s);
  vector<mint> p25(k + 1, 1);
  vector<mint> p26(k + 1, 1);
  rep(i, k) {
    p25[i + 1] = p25[i] * 25;
    p26[i + 1] = p26[i] * 26;
  }
  mint ans = 0;
  rep(i, k + 1) {
    mint res = p25[i];
    res *= modnCr(i + n - 1, n - 1, mod);
    res *= p26[k - i];
    ans += res;
  }
  cout << ans << endl;
}