Problem p02632 (C++)

Buggy submission (status: Time Limit Exceeded):
const int isDebugMode = 1;
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<long long, long long> P;
struct edge {
  long long to, cost;
};
const int inf = 1 << 27;
const long long INF = 1LL << 60;
const int COMBMAX = 1001001;
const long long MOD = 1000000007;
const long long dy[] = {-1, 0, 0, 1};
const long long dx[] = {0, -1, 1, 0};
string abc = "abcdefghijklmnopqrstuvwxyz";
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define eachdo(v, e) for (const auto &e : (v))
#define all(v) (v).begin(), (v).end()
#define lower_index(v, e)                                                      \
  (long long)distance((v).begin(), lower_bound((v).begin(), (v).end(), e))
#define upper_index(v, e)                                                      \
  (long long)distance((v).begin(), upper_bound((v).begin(), (v).end(), e))
long long mpow(long long a, long long n, long long mod = MOD) {
  long long res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}
void pt() {
  cout << endl;
  return;
}
template <class Head> void pt(Head &&head) {
  cout << head;
  pt();
  return;
}
template <class Head, class... Tail> void pt(Head &&head, Tail &&...tail) {
  cout << head << " ";
  pt(forward<Tail>(tail)...);
}
void dpt() {
  if (!isDebugMode)
    return;
  cout << endl;
  return;
}
template <class Head> void dpt(Head &&head) {
  if (!isDebugMode)
    return;
  cout << head;
  pt();
  return;
}
template <class Head, class... Tail> void dpt(Head &&head, Tail &&...tail) {
  if (!isDebugMode)
    return;
  cout << head << " ";
  pt(forward<Tail>(tail)...);
}
template <class T> void debug(T v) {
  if (!isDebugMode)
    return;
  rep(i, v.size()) cout << v[i] << " ";
  cout << endl;
}
template <class T> void debug2(T v) {
  if (!isDebugMode)
    return;
  rep(i, v.size()) {
    rep(j, v[i].size()) cout << v[i][j] << " ";
    cout << endl;
  }
}
template <class T1, class T2> inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2> inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2> long long gcd(T1 a, T2 b) {
  return a % b ? gcd(b, a % b) : b;
}
template <class T1, class T2> void reduce(T1 &a, T2 &b) {
  ll g = gcd(a, b);
  a /= g;
  b /= g;
  return;
}
bool valid(long long H, long long W, long long h, long long w) {
  return 0 <= h && h < H && 0 <= w && w < W;
}

struct mint {
  long long x;
  mint(long long x = 0) : x((x % MOD + MOD) % MOD) {}
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(long long t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  mint inv() const { return pow(MOD - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

class combination {
public:
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < MOD);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    if (COMBMAX < n) {
      mint ret = 1;
      for (long long i = 1; i <= k; i++) {
        ret *= (n - i + 1);
        ret /= i;
      }
      return ret;
    }
    return fact[n] * ifact[k] * ifact[n - k];
  }

  mint multi(long long n, long long sum, long long l, long long r) {
    long long m = r - l + 1;
    long long t = sum - n * (l - 1);
    mint ans = 0;
    for (long long k = 0; k <= (t - n) / m; k++) {
      long long sign = k % 2 == 0 ? 1 : -1;
      mint temp = this->operator()(n, k);
      temp *= this->operator()(n + (t - n - m * k - 1), t - n - m * k);
      temp *= sign;
      ans += temp;
    }
    return ans;
  }
} com(COMBMAX);

int main() {
  ll K;
  cin >> K;
  string s;
  cin >> s;
  ll N = s.size();
  mint ans = 0;
  rep(i, K + 1) {
    mint t = 0;
    t += mpow(26, i);
    t *= mpow(25, K - i);
    t *= com.multi(N, K - i, 0, INF);
    ans += t;
  }
  pt(ans.x);

  return 0;
}

Fixed submission:
const int isDebugMode = 1;
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<long long, long long> P;
struct edge {
  long long to, cost;
};
const int inf = 1 << 27;
const long long INF = 1LL << 60;
const int COMBMAX = 3000000;
const long long MOD = 1000000007;
const long long dy[] = {-1, 0, 0, 1};
const long long dx[] = {0, -1, 1, 0};
string abc = "abcdefghijklmnopqrstuvwxyz";
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define eachdo(v, e) for (const auto &e : (v))
#define all(v) (v).begin(), (v).end()
#define lower_index(v, e)                                                      \
  (long long)distance((v).begin(), lower_bound((v).begin(), (v).end(), e))
#define upper_index(v, e)                                                      \
  (long long)distance((v).begin(), upper_bound((v).begin(), (v).end(), e))
long long mpow(long long a, long long n, long long mod = MOD) {
  long long res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}
void pt() {
  cout << endl;
  return;
}
template <class Head> void pt(Head &&head) {
  cout << head;
  pt();
  return;
}
template <class Head, class... Tail> void pt(Head &&head, Tail &&...tail) {
  cout << head << " ";
  pt(forward<Tail>(tail)...);
}
void dpt() {
  if (!isDebugMode)
    return;
  cout << endl;
  return;
}
template <class Head> void dpt(Head &&head) {
  if (!isDebugMode)
    return;
  cout << head;
  pt();
  return;
}
template <class Head, class... Tail> void dpt(Head &&head, Tail &&...tail) {
  if (!isDebugMode)
    return;
  cout << head << " ";
  pt(forward<Tail>(tail)...);
}
template <class T> void debug(T v) {
  if (!isDebugMode)
    return;
  rep(i, v.size()) cout << v[i] << " ";
  cout << endl;
}
template <class T> void debug2(T v) {
  if (!isDebugMode)
    return;
  rep(i, v.size()) {
    rep(j, v[i].size()) cout << v[i][j] << " ";
    cout << endl;
  }
}
template <class T1, class T2> inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2> inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2> long long gcd(T1 a, T2 b) {
  return a % b ? gcd(b, a % b) : b;
}
template <class T1, class T2> void reduce(T1 &a, T2 &b) {
  ll g = gcd(a, b);
  a /= g;
  b /= g;
  return;
}
bool valid(long long H, long long W, long long h, long long w) {
  return 0 <= h && h < H && 0 <= w && w < W;
}

struct mint {
  long long x;
  mint(long long x = 0) : x((x % MOD + MOD) % MOD) {}
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(long long t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  mint inv() const { return pow(MOD - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

class combination {
public:
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < MOD);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    if (COMBMAX < n) {
      mint ret = 1;
      for (long long i = 1; i <= k; i++) {
        ret *= (n - i + 1);
        ret /= i;
      }
      return ret;
    }
    return fact[n] * ifact[k] * ifact[n - k];
  }

  mint multi(long long n, long long sum, long long l, long long r) {
    long long m = r - l + 1;
    long long t = sum - n * (l - 1);
    mint ans = 0;
    for (long long k = 0; k <= (t - n) / m; k++) {
      long long sign = k % 2 == 0 ? 1 : -1;
      mint temp = this->operator()(n, k);
      temp *= this->operator()(n + (t - n - m * k - 1), t - n - m * k);
      temp *= sign;
      ans += temp;
    }
    return ans;
  }
} com(COMBMAX);

int main() {
  ll K;
  cin >> K;
  string s;
  cin >> s;
  ll N = s.size();
  mint ans = 0;
  rep(i, K + 1) {
    mint t = 0;
    t += mpow(26, i);
    t *= mpow(25, K - i);
    t *= com.multi(N, K - i, 0, INF);
    ans += t;
  }
  pt(ans.x);

  return 0;
}