Problem p02625 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define ll long long
#define ar array
#define AC                                                                     \
  ios_base::sync_with_stdio(0);                                                \
  cin.tie(NULL);
using namespace std;
const int MOD = 1e9 + 7;
const int N = 5 * 1e5;

struct mi {
  ll v;
  explicit operator ll() const { return v; }
  mi() { v = 0; }
  mi(ll _v) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0)
      v += MOD;
  }
  friend bool operator==(const mi &a, const mi &b) { return a.v == b.v; }
  friend bool operator!=(const mi &a, const mi &b) { return !(a == b); }
  friend bool operator<(const mi &a, const mi &b) { return a.v < b.v; }

  mi &operator+=(const mi &m) {
    if ((v += m.v) >= MOD)
      v -= MOD;
    return *this;
  }
  mi &operator-=(const mi &m) {
    if ((v -= m.v) < 0)
      v += MOD;
    return *this;
  }
  mi &operator*=(const mi &m) {
    v = v * m.v % MOD;
    return *this;
  }
  mi &operator/=(const mi &m) { return (*this) *= inv(m); }
  friend mi pow(mi a, ll p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1)
        ans *= a;
    return ans;
  }
  friend mi inv(const mi &a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }

  mi operator-() const { return mi(-v); }
  mi &operator++() { return *this += 1; }
  mi &operator--() { return *this -= 1; }
  mi operator++(int) {
    mi temp;
    temp.v = v++;
    return temp;
  }
  mi operator--(int) {
    mi temp;
    temp.v = v--;
    return temp;
  }
  friend mi operator+(mi a, const mi &b) { return a += b; }
  friend mi operator-(mi a, const mi &b) { return a -= b; }
  friend mi operator*(mi a, const mi &b) { return a *= b; }
  friend mi operator/(mi a, const mi &b) { return a /= b; }
  friend ostream &operator<<(ostream &os, const mi &m) {
    os << m.v;
    return os;
  }
  friend istream &operator>>(istream &is, mi &m) {
    ll x;
    is >> x;
    m.v = x;
    return is;
  }
};

int n, m;
mi fac[N];
mi facInv[N];

void initFac() {
  fac[0] = 1;
  facInv[0] = 1;
  for (int i = 1; i <= m; i++) {
    fac[i] = fac[i - 1] * i;
    facInv[i] = inv(fac[i]);
  }
}

mi choose(int n, int k) {
  if (k < 0)
    return 0;
  if (n < 0)
    return 0;
  if (k > n)
    return 0;

  mi res = fac[n] * facInv[n - k] * facInv[k];
  return res;
}

int main() {
  AC cin >> n >> m;
  initFac();
  mi res = 0;
  mi cur = 1;
  for (int k = 0; k <= n; k++) {
    res += cur * choose(n, k) * choose(m - k, n - k) * fac[n - k];
    cur = -cur;
  }

  cout << res * choose(m, n) * fac[n] << endl;
}

Fixed submission:
#include <bits/stdc++.h>
#define ll long long
#define ar array
#define AC                                                                     \
  ios_base::sync_with_stdio(0);                                                \
  cin.tie(NULL);
using namespace std;
const int MOD = 1e9 + 7;
const int N = 5 * 1e5;

struct mi {
  ll v;
  explicit operator ll() const { return v; }
  mi() { v = 0; }
  mi(ll _v) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0)
      v += MOD;
  }
  friend bool operator==(const mi &a, const mi &b) { return a.v == b.v; }
  friend bool operator!=(const mi &a, const mi &b) { return !(a == b); }
  friend bool operator<(const mi &a, const mi &b) { return a.v < b.v; }

  mi &operator+=(const mi &m) {
    if ((v += m.v) >= MOD)
      v -= MOD;
    return *this;
  }
  mi &operator-=(const mi &m) {
    if ((v -= m.v) < 0)
      v += MOD;
    return *this;
  }
  mi &operator*=(const mi &m) {
    v = v * m.v % MOD;
    return *this;
  }
  mi &operator/=(const mi &m) { return (*this) *= inv(m); }
  friend mi pow(mi a, ll p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1)
        ans *= a;
    return ans;
  }
  friend mi inv(const mi &a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }

  mi operator-() const { return mi(-v); }
  mi &operator++() { return *this += 1; }
  mi &operator--() { return *this -= 1; }
  mi operator++(int) {
    mi temp;
    temp.v = v++;
    return temp;
  }
  mi operator--(int) {
    mi temp;
    temp.v = v--;
    return temp;
  }
  friend mi operator+(mi a, const mi &b) { return a += b; }
  friend mi operator-(mi a, const mi &b) { return a -= b; }
  friend mi operator*(mi a, const mi &b) { return a *= b; }
  friend mi operator/(mi a, const mi &b) { return a /= b; }
  friend ostream &operator<<(ostream &os, const mi &m) {
    os << m.v;
    return os;
  }
  friend istream &operator>>(istream &is, mi &m) {
    ll x;
    is >> x;
    m.v = x;
    return is;
  }
};

int n, m;
mi fac[N + 5];
mi facInv[N + 5];

void initFac() {
  fac[0] = 1;
  facInv[0] = 1;
  for (int i = 1; i <= m; i++) {
    fac[i] = fac[i - 1] * i;
    facInv[i] = inv(fac[i]);
  }
}

mi choose(int n, int k) {
  if (k < 0)
    return 0;
  if (n < 0)
    return 0;
  if (k > n)
    return 0;

  mi res = fac[n] * facInv[n - k] * facInv[k];
  return res;
}

int main() {
  AC cin >> n >> m;
  initFac();
  mi res = 0;
  mi cur = 1;
  for (int k = 0; k <= n; k++) {
    res += cur * choose(n, k) * choose(m - k, n - k) * fac[n - k];
    cur = -cur;
  }

  cout << res * choose(m, n) * fac[n] << endl;
}