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

#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;

// template {{{  0
// using {{{ 1
using ll = long long int;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vii = vector<pii>;
using vll = vector<pll>;
// }}} 1
// definition {{{ 1
// scaning {{{ 2
#define Scd(x) scanf("%d", &x)
#define Scd2(x, y) scanf("%d%d", &x, &y)
#define Scd3(x, y, z) scanf("%d%d%d", &x, &y, &z)
#define Scll(x) scanf("%lld", &x)
#define Scll2(x, y) scanf("%lld%lld", &x, &y)
#define Scll3(x, y, z) scanf("%lld%lld%lld", &x, &y, &z)
#define Scc(c) scanf("%c", &c);
#define Scs(s) scanf("%s", s);
#define Scstr(s) scanf("%s", &s);
// }}} 2
// constants {{{ 2
#define EPS (1e-7)
#define INF (2e9)
#define PI (acos(-1))
// }}} 2
// systems {{{ 2
#define Repe(x, y, z) for (ll x = z; x < y; x++)
#define Rep(x, y) Repe(x, y, 0)
#define RRepe(x, y, z) for (ll x = y - z - 1; x >= 0; x--)
#define RRep(x, y) RRepe(x, y, 0)
// }}} 2
// output {{{ 2
#define YesNo(a) (a) ? printf("Yes\\n") : printf("No\\n")
#define YESNO(a) (a) ? printf("YES\\n") : printf("NO\\n")
// }}} 2
// }}} 1
// input {{{ 1
// }}} 1
// }}} 0

const long long int mod = 1000000007;

// PowMod( base, index, modulo) return base ** index % modulo {{{
// PowMod = base ** index % mod ( natural numbers )
inline constexpr long long int PowMod(long long int base, long long int index,
                                      long long int modulo = mod) {
  if (index == 0)
    return 1;
  // O( log(index) )
  if (index % 2) {
    return base * PowMod(base, index - 1, modulo) % modulo;
  } else {
    long long int Phalf = index / 2;
    long long int half = PowMod(base, Phalf, modulo);
    return half * half % modulo;
  }
}
// }}}
// CombMod( n, r, modulo ) return nCr % modulo {{{
// CombMod(ination) = nCr % mod ( natural number )
inline constexpr long long int CombMod(long long int n, long long int r,
                                       long long int modulo = mod) {
  if (n < r)
    return CombMod(r, n, modulo);
  long long int Upper = 1;
  long long int Lower = 1;
  for (long long int i = 0; i < r; i++) {
    Upper = Upper * (n - i) % modulo;
    Lower = Lower * (i + 1) % modulo;
  }
  // Return (Upper / Lower)
  long long int ret = Upper * PowMod(Lower, modulo - 2, modulo) % modulo;
  return ret;
}
// }}}
// FactMod( n, modulo ) return n! % modulo {{{
// Fact(orial) = n! % mod ( natural number )
inline constexpr long long int Fact(long long int n,
                                    long long int modulo = mod) {
  long long int Upper = 1;
  for (long long int i = 0; i < n; i++) {
    Upper = Upper * (n - i) % modulo;
  }
  return Upper;
}
// }}}
// modint {{{

struct modint {
  long long int a;
  inline constexpr modint(long long int x = 0) noexcept : a(x % mod) {}
  inline constexpr long long int &value() noexcept { return a; }
  inline constexpr const long long int &value() const noexcept { return a; }
  inline constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  inline constexpr modint operator+(const int rhs) const noexcept {
    return modint(*this) += rhs;
  }
  inline constexpr modint operator+(const long long int rhs) const noexcept {
    return modint(*this) += rhs;
  }
  inline constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  inline constexpr modint operator-(const int rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  inline constexpr modint operator-(const long long int rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  inline constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  inline constexpr modint operator*(const int rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  inline constexpr modint operator*(const long long int rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  inline constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  inline constexpr modint operator/(const int rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  inline constexpr modint operator/(const long long int rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  inline constexpr modint operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= mod)
      a -= mod;
    return *this;
  }
  inline constexpr modint operator-=(const modint rhs) noexcept {
    a -= rhs.a;
    if (a < 0)
      a += mod;
    return *this;
  }
  inline constexpr modint operator*=(const modint rhs) noexcept {
    a = a * rhs.a % mod;
    return *this;
  }
  inline constexpr modint operator/=(const modint rhs) noexcept {
    a = a * PowMod(rhs.a, mod - 2) % mod;
    return *this;
  }
};

// }}}

int main() {

  int K;
  static char s[1111111];
  Scd(K);
  Scs(s);
  int N = strlen(s);

  vector<modint> f(2e6 + 100, 1);
  vector<modint> fr(2e6 + 100, 1);
  Rep(i, N + K + 1) f[i + 1] = f[i] * (i + 1), fr[i] /= f[i];

  modint ans = 0;
  modint t25 = 1;
  Rep(i, K + 1) {
    ans += f[i + N - 1] * fr[i] * fr[N - 1] * t25 * PowMod(26, K - i);
    t25 *= 25;
  }

  printf("%lld\\n", ans);
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;

// template {{{  0
// using {{{ 1
using ll = long long int;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vii = vector<pii>;
using vll = vector<pll>;
// }}} 1
// definition {{{ 1
// scaning {{{ 2
#define Scd(x) scanf("%d", &x)
#define Scd2(x, y) scanf("%d%d", &x, &y)
#define Scd3(x, y, z) scanf("%d%d%d", &x, &y, &z)
#define Scll(x) scanf("%lld", &x)
#define Scll2(x, y) scanf("%lld%lld", &x, &y)
#define Scll3(x, y, z) scanf("%lld%lld%lld", &x, &y, &z)
#define Scc(c) scanf("%c", &c);
#define Scs(s) scanf("%s", s);
#define Scstr(s) scanf("%s", &s);
// }}} 2
// constants {{{ 2
#define EPS (1e-7)
#define INF (2e9)
#define PI (acos(-1))
// }}} 2
// systems {{{ 2
#define Repe(x, y, z) for (ll x = z; x < y; x++)
#define Rep(x, y) Repe(x, y, 0)
#define RRepe(x, y, z) for (ll x = y - z - 1; x >= 0; x--)
#define RRep(x, y) RRepe(x, y, 0)
// }}} 2
// output {{{ 2
#define YesNo(a) (a) ? printf("Yes\\n") : printf("No\\n")
#define YESNO(a) (a) ? printf("YES\\n") : printf("NO\\n")
// }}} 2
// }}} 1
// input {{{ 1
// }}} 1
// }}} 0

const long long int mod = 1000000007;

// PowMod( base, index, modulo) return base ** index % modulo {{{
// PowMod = base ** index % mod ( natural numbers )
inline constexpr long long int PowMod(long long int base, long long int index,
                                      long long int modulo = mod) {
  if (index == 0)
    return 1;
  // O( log(index) )
  if (index % 2) {
    return base * PowMod(base, index - 1, modulo) % modulo;
  } else {
    long long int Phalf = index / 2;
    long long int half = PowMod(base, Phalf, modulo);
    return half * half % modulo;
  }
}
// }}}
// CombMod( n, r, modulo ) return nCr % modulo {{{
// CombMod(ination) = nCr % mod ( natural number )
inline constexpr long long int CombMod(long long int n, long long int r,
                                       long long int modulo = mod) {
  if (n < r)
    return CombMod(r, n, modulo);
  long long int Upper = 1;
  long long int Lower = 1;
  for (long long int i = 0; i < r; i++) {
    Upper = Upper * (n - i) % modulo;
    Lower = Lower * (i + 1) % modulo;
  }
  // Return (Upper / Lower)
  long long int ret = Upper * PowMod(Lower, modulo - 2, modulo) % modulo;
  return ret;
}
// }}}
// FactMod( n, modulo ) return n! % modulo {{{
// Fact(orial) = n! % mod ( natural number )
inline constexpr long long int Fact(long long int n,
                                    long long int modulo = mod) {
  long long int Upper = 1;
  for (long long int i = 0; i < n; i++) {
    Upper = Upper * (n - i) % modulo;
  }
  return Upper;
}
// }}}
// modint {{{

struct modint {
  long long int a;
  inline constexpr modint(long long int x = 0) noexcept : a(x % mod) {}
  inline constexpr long long int &value() noexcept { return a; }
  inline constexpr const long long int &value() const noexcept { return a; }
  inline constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  inline constexpr modint operator+(const int rhs) const noexcept {
    return modint(*this) += rhs;
  }
  inline constexpr modint operator+(const long long int rhs) const noexcept {
    return modint(*this) += rhs;
  }
  inline constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  inline constexpr modint operator-(const int rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  inline constexpr modint operator-(const long long int rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  inline constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  inline constexpr modint operator*(const int rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  inline constexpr modint operator*(const long long int rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  inline constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  inline constexpr modint operator/(const int rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  inline constexpr modint operator/(const long long int rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  inline constexpr modint operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= mod)
      a -= mod;
    return *this;
  }
  inline constexpr modint operator-=(const modint rhs) noexcept {
    a -= rhs.a;
    if (a < 0)
      a += mod;
    return *this;
  }
  inline constexpr modint operator*=(const modint rhs) noexcept {
    a = a * rhs.a % mod;
    return *this;
  }
  inline constexpr modint operator/=(const modint rhs) noexcept {
    a = a * PowMod(rhs.a, mod - 2) % mod;
    return *this;
  }
};

// }}}

int main() {

  int K;
  static char s[1111111];
  Scd(K);
  Scs(s);
  int N = strlen(s);

  vector<modint> f(2e6 + 100, 1);
  Rep(i, N + K + 1) f[i + 1] = f[i] * (i + 1);

  modint ans = 0;
  Rep(i, K + 1) {
    ans += f[i + N - 1] / f[i] / f[N - 1] * PowMod(25, i) * PowMod(26, K - i);
  }

  printf("%lld\\n", ans);
}