Problem p02632 (C++) — buggy submission, verdict: Runtime Error

/*
    Author : DemonStar
*/

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
#define ordered_set                                                            \\
  tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update>
#define fast                                                                   \\
  ios_base::sync_with_stdio(0);                                                \\
  cin.tie(0);                                                                  \\
  cout.tie(0);
#define all(x) x.begin(), x.end()
#define loop(i, n) for (ll i = 0; i < n; i++)
#define pl pair<ll, ll>
#define vl vector<ll>
#define endl '\\n'
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\\'' << x << '\\''; }
void __print(const char *x) { cerr << '\\"' << x << '\\"'; }
void __print(const string &x) { cerr << '\\"' << x << '\\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }

template <typename T, typename V> void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T> void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x)
    cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\\n"; }
template <typename T, typename... V> void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v))
    cerr << ", ";
  _print(v...);
}

#ifdef LOCAL
#define debug(x...)                                                            \\
  cerr << "[" << #x << "] = [";                                                \\
  _print(x)
#else
#define debug(x...)
#endif

struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};

template <typename T, typename TT>
ostream &operator<<(ostream &os, const pair<T, TT> &t) {
  return os << t.first << " " << t.second;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &t) {
  for (auto &i : t)
    os << i << " ";
  return os;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &t : v)
    is >> t;
  return is;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, vector<pair<T1, T2>> &v) {
  for (pair<T1, T2> &t : v)
    is >> t.first >> t.second;
  return is;
}

const ll mod = 1e9 + 7;

ll modpow(ll n, ll p) {
  ll ans = 1;
  while (p) {
    if (p & 1)
      (ans *= n) %= mod;
    (n *= n) %= mod, p /= 2;
  }
  return ans;
}

int main() {

#ifdef LOCAL
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif

  ll k;
  string s;
  cin >> k >> s;
  ll n = s.size() + k;
  vl fact(2e6 + 5), inv(2e6 + 5);
  fact[0] = 1, inv[0] = 1;
  for (int i = 1; i < 2e6 + 5; i++) {
    fact[i] = (fact[i - 1] * i) % mod;
    inv[i] = modpow(fact[i], mod - 2);
  }
  ll ans = modpow(26, n);
  for (int m = 0; m < s.size(); m++) {
    ll neg = (fact[n] * inv[m]) % mod;
    (neg *= inv[n - m]) %= mod;
    (neg *= modpow(25, n - m)) %= mod;
    ans = (mod * mod + ans - neg) % mod;
  }
  cout << ans << endl;

#ifdef LOCAL
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s";
#endif

  return 0;
}

Error: 0

Fixed submission:

/*
    Author : DemonStar
*/

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
#define ordered_set                                                            \\
  tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update>
#define fast                                                                   \\
  ios_base::sync_with_stdio(0);                                                \\
  cin.tie(0);                                                                  \\
  cout.tie(0);
#define all(x) x.begin(), x.end()
#define loop(i, n) for (ll i = 0; i < n; i++)
#define pl pair<ll, ll>
#define vl vector<ll>
#define endl '\\n'
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\\'' << x << '\\''; }
void __print(const char *x) { cerr << '\\"' << x << '\\"'; }
void __print(const string &x) { cerr << '\\"' << x << '\\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }

template <typename T, typename V> void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T> void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x)
    cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\\n"; }
template <typename T, typename... V> void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v))
    cerr << ", ";
  _print(v...);
}

#ifdef LOCAL
#define debug(x...)                                                            \\
  cerr << "[" << #x << "] = [";                                                \\
  _print(x)
#else
#define debug(x...)
#endif

struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};

template <typename T, typename TT>
ostream &operator<<(ostream &os, const pair<T, TT> &t) {
  return os << t.first << " " << t.second;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &t) {
  for (auto &i : t)
    os << i << " ";
  return os;
}
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &t : v)
    is >> t;
  return is;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, vector<pair<T1, T2>> &v) {
  for (pair<T1, T2> &t : v)
    is >> t.first >> t.second;
  return is;
}

const ll mod = 1e9 + 7;

ll modpow(ll n, ll p) {
  ll ans = 1;
  while (p) {
    if (p & 1)
      (ans *= n) %= mod;
    (n *= n) %= mod, p /= 2;
  }
  return ans;
}

int main() {

#ifdef LOCAL
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif

  ll k;
  string s;
  cin >> k >> s;
  ll n = s.size() + k;
  vl fact(1e6 + 5), inv(1e6 + 5);
  fact[0] = 1, inv[0] = 1;
  for (int i = 1; i < 1e6 + 5; i++) {
    fact[i] = (fact[i - 1] * i) % mod;
    inv[i] = modpow(fact[i], mod - 2);
  }
  ll ans = modpow(26, n);
  for (int m = 0; m < s.size(); m++) {
    ll neg = (fact[n] * inv[m]) % mod;
    (neg *= inv[n - m]) %= mod;
    (neg *= modpow(25, n - m)) %= mod;
    ans = (mod * mod + ans - neg) % mod;
  }
  cout << ans << endl;

#ifdef LOCAL
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s";
#endif

  return 0;
}