Problem p02625 (C++) — buggy submission, verdict: Runtime Error

// Nihal Mittal - nihal_47
// Strike First , Strike Hard , No Mercy !!

/**⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⠀⠙⣿⣿⣿⣷⢳⢀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢀
⠀⠀⣸⣿⣿⣿⠸⠀⠀⠀⠒⠒⠒⠐⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀
⠀⣴⣿⣿⣿⡿⠀⠒⣋⣙⡒⢰⠀⠤⣖⠒⢾⣿⣿⣿⣿⣧⠀⠀
⢺⣿⣿⣿⣿⢀⠀⠀⠉⠉⠉⠸⠀⡇⠉⠉⠀⢿⣿⣿⣿⣄⠀⠀
⠀⠙⣿⣿⣧⢻⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⣸⠸⣿⣿⠿⠰⠀
⠀⠀⠀⠹⣿⣿⣿⣷⠀⡠⠙⣲⣔⣅⢡⣰⣷⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⠀⡿⠭⠭⠭⠭⢿⠀⣿⢻⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠙⠛⣿⢻⠹⣿⠐⠙⠛⠟⠉⢀⣴⡟⢿⣿⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠻⣦⣤⣶⠾⠋⠀⠀⠁⡦⢄⢀⠀⠀⠀
⠀⠀⠀⠀⡠⠁⡇⠑⢄⠀⠀⠀⠀⠀⠀⠔⠀⠀⠁⠀⠀⠀⠉⠁
⠀⠔⠊⠁⠀⠀⣇⠀⠀⠀⠑⡤⠤⢎⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢢⠠⠀⡠⢆⠀⠀⡠⠙⢄⠀⡸⠀
**/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define mk make_pair
#define pb push_back
#define in insert
#define se second
#define fi first
#define mod 1000000007
#define watch(x) cout << (#x) << " is " << (x) << "\\n"
#define all(v) (v).begin(), (v).end()
#define fast                                                                   \\
  ios_base::sync_with_stdio(false);                                            \\
  cin.tie(NULL);                                                               \\
  cout.tie(0);
#define pii pair<ll, ll>
#define vi(x) vector<x>
#define maxn 100005
#define ordered_set                                                            \\
  tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update>
using namespace std;
using namespace __gnu_pbds;
ll fac[500010];
ll power(ll x, ll y) {
  ll res = 1;
  x = x % mod;
  while (y > 0) {
    if (y & 1)
      res = (res * x) % mod;
    y = y >> 1;
    x = (x * x) % mod;
  }
  return res;
}
ll modInverse(ll n, ll p) { return power(n, p - 2); }
void precompute() {
  fac[0] = 1;
  for (ll i = 1; i <= 500003; i++)
    fac[i] = fac[i - 1] * i % mod;
}
ll ncr(ll n, ll r) {
  if (r == 0)
    return 1;

  return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod) %
          mod) %
         mod;
}
signed main() {
  fast;

  ll n, m, j, ans = 0, cur = 1;
  precompute();
  cin >> n >> m;
  for (j = 0; j <= n; j++) {
    ll a = ncr(n, j);
    a *= ncr(m - j, n - j);
    a %= mod;
    a *= fac[n - j];
    a %= mod;
    if (j & 1)
      ans = (ans - a + mod) % mod;
    else
      ans = (ans + a) % mod;
  }
  ans = (ans * ncr(m, n)) % mod;
  ans = (ans * fac[n]) % mod;
  cout << ans;
}

Error: WA

Fixed submission:

// Nihal Mittal - nihal_47
// Strike First , Strike Hard , No Mercy !!

/**⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⠀⠙⣿⣿⣿⣷⢳⢀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢀
⠀⠀⣸⣿⣿⣿⠸⠀⠀⠀⠒⠒⠒⠐⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀
⠀⣴⣿⣿⣿⡿⠀⠒⣋⣙⡒⢰⠀⠤⣖⠒⢾⣿⣿⣿⣿⣧⠀⠀
⢺⣿⣿⣿⣿⢀⠀⠀⠉⠉⠉⠸⠀⡇⠉⠉⠀⢿⣿⣿⣿⣄⠀⠀
⠀⠙⣿⣿⣧⢻⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⣸⠸⣿⣿⠿⠰⠀
⠀⠀⠀⠹⣿⣿⣿⣷⠀⡠⠙⣲⣔⣅⢡⣰⣷⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⣼⣿⣿⣿⣿⠀⡿⠭⠭⠭⠭⢿⠀⣿⢻⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠙⠛⣿⢻⠹⣿⠐⠙⠛⠟⠉⢀⣴⡟⢿⣿⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠻⣦⣤⣶⠾⠋⠀⠀⠁⡦⢄⢀⠀⠀⠀
⠀⠀⠀⠀⡠⠁⡇⠑⢄⠀⠀⠀⠀⠀⠀⠔⠀⠀⠁⠀⠀⠀⠉⠁
⠀⠔⠊⠁⠀⠀⣇⠀⠀⠀⠑⡤⠤⢎⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢢⠠⠀⡠⢆⠀⠀⡠⠙⢄⠀⡸⠀
**/
#include <bits/stdc++.h>

#define ll long long
#define ld long double
#define mk make_pair
#define pb push_back
#define in insert
#define se second
#define fi first
#define mod 1000000007
#define watch(x) cout << (#x) << " is " << (x) << "\\n"
#define all(v) (v).begin(), (v).end()
#define fast                                                                   \\
  ios_base::sync_with_stdio(false);                                            \\
  cin.tie(NULL);                                                               \\
  cout.tie(0);
#define pii pair<ll, ll>
#define vi(x) vector<x>
#define maxn 100005

using namespace std;

ll fac[600010];
ll power(ll x, ll y) {
  ll res = 1;
  x = x % mod;
  while (y > 0) {
    if (y & 1)
      res = (res * x) % mod;
    y = y >> 1;
    x = (x * x) % mod;
  }
  return res;
}
ll modInverse(ll n, ll p) { return power(n, p - 2); }
ll precompute() {
  fac[0] = 1;
  for (ll i = 1; i <= 600008; i++)
    fac[i] = fac[i - 1] * i % mod;
}
ll ncr(ll n, ll r) {
  if (r == 0)
    return 1;

  return (fac[n] * modInverse(fac[r], mod) % mod * modInverse(fac[n - r], mod) %
          mod) %
         mod;
}
signed main() {
  fast;

  ll n, m, j, ans = 0, cur = 1;
  precompute();
  cin >> n >> m;
  for (j = 0; j <= n; j++) {
    ll a = ncr(n, j);
    a *= ncr(m - j, n - j);
    a %= mod;
    a *= fac[n - j];
    a %= mod;
    if (j & 1)
      ans -= a;
    else
      ans += a;
    ans %= mod;
  }
  ans = (ans * ncr(m, n) % mod) % mod;
  ans = (ans * fac[n] % mod) % mod;
  cout << ans;
}