Problem p03152 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> P;
typedef pair<int, int> Pi;
#define rep(i, n) for (ll i = 0; i < n; i++)
#define FOR(i, a, b) for (ll i = a; i < b; i++)
#define fi first
#define se second

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T> ostream &operator<<(ostream &s, const complex<T> &d) {
  return s << "(" << d.real() << ", " << d.imag() << ")";
}
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const pair<T1, T2> &d) {
  return s << "(" << d.first << ", " << d.second << ")";
}
template <typename T> ostream &operator<<(ostream &s, const vector<T> &d) {
  int len = d.size();
  rep(i, len) {
    s << d[i];
    if (i < len - 1)
      s << " ";
  }
  return s;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<vector<T>> &d) {
  int len = d.size();
  rep(i, len) { s << d[i] << endl; }
  return s;
}
template <typename T> ostream &operator<<(ostream &s, const set<T> &v) {
  s << "{ ";
  for (auto itr = v.begin(); itr != v.end(); ++itr) {
    if (itr != v.begin()) {
      s << ", ";
    }
    s << (*itr);
  }
  s << " }";
  return s;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const map<T1, T2> &m) {
  s << "{" << endl;
  for (auto itr = m.begin(); itr != m.end(); ++itr) {
    s << " " << (*itr).first << " : " << (*itr).second << endl;
  }
  s << "}" << endl;
  return s;
}

const ll mod = 1e9 + 7;
const ll inf = 1e15;
const int INF = 1e9;
const double PI = acos(-1);
const double EPS = 1e-10;

struct mint {
  ll x;
  mint(ll 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(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  // for prime mod
  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;
  }
};

struct combination {
  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;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<int> a(n), b(n);
  set<int> flag1, flag2;
  rep(i, n) {
    cin >> a[i];
    flag1.insert(a[i]);
  }
  rep(i, m) {
    cin >> b[i];
    flag2.insert(b[i]);
  }
  if (flag1.size() != n || flag2.size() != m) {
    cout << 0 << endl;
    return 0;
  }
  sort(begin(a), end(a));
  sort(begin(b), end(b));
  mint ans = 1;
  for (int i = n * m; i >= 1; i--) {
    bool f1 = flag1.count(i), f2 = flag2.count(i);
    if (f1 && f2)
      continue;
    else if (f1 && !f2) {
      ans *= end(b) - upper_bound(begin(b), end(b), i);
    } else if (!f1 && f2) {
      ans *= end(a) - upper_bound(begin(a), end(a), i);
    } else {
      ans *= (end(b) - upper_bound(begin(b), end(b), i)) *
                 (end(a) - upper_bound(begin(a), end(a), i)) -
             (n * m - i);
    }
  }
  cout << ans.x << endl;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> P;
typedef pair<int, int> Pi;
#define rep(i, n) for (ll i = 0; i < n; i++)
#define FOR(i, a, b) for (ll i = a; i < b; i++)
#define fi first
#define se second

template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T> ostream &operator<<(ostream &s, const complex<T> &d) {
  return s << "(" << d.real() << ", " << d.imag() << ")";
}
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const pair<T1, T2> &d) {
  return s << "(" << d.first << ", " << d.second << ")";
}
template <typename T> ostream &operator<<(ostream &s, const vector<T> &d) {
  int len = d.size();
  rep(i, len) {
    s << d[i];
    if (i < len - 1)
      s << " ";
  }
  return s;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<vector<T>> &d) {
  int len = d.size();
  rep(i, len) { s << d[i] << endl; }
  return s;
}
template <typename T> ostream &operator<<(ostream &s, const set<T> &v) {
  s << "{ ";
  for (auto itr = v.begin(); itr != v.end(); ++itr) {
    if (itr != v.begin()) {
      s << ", ";
    }
    s << (*itr);
  }
  s << " }";
  return s;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const map<T1, T2> &m) {
  s << "{" << endl;
  for (auto itr = m.begin(); itr != m.end(); ++itr) {
    s << " " << (*itr).first << " : " << (*itr).second << endl;
  }
  s << "}" << endl;
  return s;
}

const ll mod = 1e9 + 7;
const ll inf = 1e15;
const int INF = 1e9;
const double PI = acos(-1);
const double EPS = 1e-10;

struct mint {
  ll x;
  mint(ll 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(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }
  // for prime mod
  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;
  }
};

struct combination {
  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;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<int> a(n), b(m);
  set<int> flag1, flag2;
  rep(i, n) {
    cin >> a[i];
    flag1.insert(a[i]);
  }
  rep(i, m) {
    cin >> b[i];
    flag2.insert(b[i]);
  }
  if (flag1.size() != n || flag2.size() != m) {
    cout << 0 << endl;
    return 0;
  }
  sort(begin(a), end(a));
  sort(begin(b), end(b));
  mint ans = 1;
  for (int i = n * m; i >= 1; i--) {
    bool f1 = flag1.count(i), f2 = flag2.count(i);
    if (f1 && f2)
      continue;
    else if (f1 && !f2) {
      ans *= end(b) - upper_bound(begin(b), end(b), i);
    } else if (!f1 && f2) {
      ans *= end(a) - upper_bound(begin(a), end(a), i);
    } else {
      ans *= (end(b) - upper_bound(begin(b), end(b), i)) *
                 (end(a) - upper_bound(begin(a), end(a), i)) -
             (n * m - i);
    }
  }
  cout << ans.x << endl;
}