Problem p02625 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int N = 1e5 + 5, MOD = 1e9 + 7;

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;
  }
};

mi facs[N], facInvs[N];

mi nCr(mi a, mi b) {
  if ((ll)b > (ll)a)
    return 0;
  if ((ll)a < 0)
    return 0;
  if ((ll)b < 0)
    return 0;
  mi cur = facs[(ll)a];
  cur = cur * facInvs[(ll)b];
  cur = cur * facInvs[(ll)a - (ll)b];
  return cur;
}

void initFacs() {
  facs[0] = 1;
  facInvs[0] = 1;
  for (int i = 1; i < N; i++) {
    facs[i] = (facs[i - 1] * i);
    facInvs[i] = inv(facs[i]);
  }
}

int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  initFacs();
  int n, m;
  cin >> n >> m;
  mi ans = 0, cur = 1;
  for (int i = 0; i <= n; i++) {
    ans += cur * facs[n - i] * nCr(m - i, n - i) * nCr(n, i);
    cur = -cur;
  }
  cout << ans * facs[n] * nCr(m, n) << "\n";
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int N = 5e5 + 5, MOD = 1e9 + 7;

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;
  }
};

mi facs[N], facInvs[N];

mi nCr(mi a, mi b) {
  if ((ll)b > (ll)a)
    return 0;
  if ((ll)a < 0)
    return 0;
  if ((ll)b < 0)
    return 0;
  mi cur = facs[(ll)a];
  cur = cur * facInvs[(ll)b];
  cur = cur * facInvs[(ll)a - (ll)b];
  return cur;
}

void initFacs() {
  facs[0] = 1;
  facInvs[0] = 1;
  for (int i = 1; i < N; i++) {
    facs[i] = (facs[i - 1] * i);
    facInvs[i] = inv(facs[i]);
  }
}

int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  initFacs();
  int n, m;
  cin >> n >> m;
  mi ans = 0, cur = 1;
  for (int i = 0; i <= n; i++) {
    ans += cur * facs[n - i] * nCr(m - i, n - i) * nCr(n, i);
    cur = -cur;
  }
  cout << ans * facs[n] * nCr(m, n) << "\n";
  return 0;
}