Problem p03152 (C++)

Buggy submission (status: Runtime Error):
#include "bits/stdc++.h"
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template <class T> constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template <class T> constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char> T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char> T_char TU(T_char cX) { return toupper(cX); };
typedef pair<LL, LL> pii;
const int vy[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          vx[] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
int popcnt(unsigned long long n) {
  int cnt = 0;
  for (int i = 0; i < 64; i++)
    if ((n >> i) & 1)
      cnt++;
  return cnt;
}
int d_sum(LL n) {
  int ret = 0;
  while (n > 0) {
    ret += n % 10;
    n /= 10;
  }
  return ret;
}
int d_cnt(LL n) {
  int ret = 0;
  while (n > 0) {
    ret++;
    n /= 10;
  }
  return ret;
}
LL gcd(LL a, LL b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
};
LL lcm(LL a, LL b) {
  LL g = gcd(a, b);
  return a / g * b;
};
#define ALL(qpqpq) (qpqpq).begin(), (qpqpq).end()
#define UNIQUE(wpwpw)                                                          \
  sort(ALL((wpwpw)));                                                          \
  (wpwpw).erase(unique(ALL((wpwpw))), (wpwpw).end())
#define LOWER(epepe) transform(ALL((epepe)), (epepe).begin(), TL<char>)
#define UPPER(rprpr) transform(ALL((rprpr)), (rprpr).begin(), TU<char>)
#define FOR(i, tptpt, ypypy) for (LL i = (tptpt); i < (ypypy); i++)
#define REP(i, upupu) FOR(i, 0, upupu)
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0)

int n, m;
bool a[1010], b[1010];
int aa, bb;
const int mod = 1e9 + 7;
int pa, pb;

int main() {
  INIT;
  cin >> n >> m;
  REP(i, n) {
    cin >> aa;
    a[aa] = 1;
  }
  REP(i, m) {
    cin >> bb;
    b[bb] = 1;
  }
  LL ans = 1;
  for (int i = n * m; i >= 1; i--) {
    if (!a[i] && !b[i]) {
      (ans *= pa * pb - (n * m - i)) %= mod;
    } else {
      if (a[i])
        pa++;
      if (b[i])
        pb++;
      if (a[i] && b[i])
        continue;
      else if (a[i])
        (ans *= pb) %= mod;
      else if (b[i])
        (ans *= pa) %= mod;
    }
  }
  cout << ans << endl;
}

Fixed submission:
#include "bits/stdc++.h"
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template <class T> constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template <class T> constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char> T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char> T_char TU(T_char cX) { return toupper(cX); };
typedef pair<LL, LL> pii;
const int vy[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          vx[] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
int popcnt(unsigned long long n) {
  int cnt = 0;
  for (int i = 0; i < 64; i++)
    if ((n >> i) & 1)
      cnt++;
  return cnt;
}
int d_sum(LL n) {
  int ret = 0;
  while (n > 0) {
    ret += n % 10;
    n /= 10;
  }
  return ret;
}
int d_cnt(LL n) {
  int ret = 0;
  while (n > 0) {
    ret++;
    n /= 10;
  }
  return ret;
}
LL gcd(LL a, LL b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
};
LL lcm(LL a, LL b) {
  LL g = gcd(a, b);
  return a / g * b;
};
#define ALL(qpqpq) (qpqpq).begin(), (qpqpq).end()
#define UNIQUE(wpwpw)                                                          \
  sort(ALL((wpwpw)));                                                          \
  (wpwpw).erase(unique(ALL((wpwpw))), (wpwpw).end())
#define LOWER(epepe) transform(ALL((epepe)), (epepe).begin(), TL<char>)
#define UPPER(rprpr) transform(ALL((rprpr)), (rprpr).begin(), TU<char>)
#define FOR(i, tptpt, ypypy) for (LL i = (tptpt); i < (ypypy); i++)
#define REP(i, upupu) FOR(i, 0, upupu)
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0)

int n, m;
bool a[1010101], b[1010101];
int aa, bb;
const int mod = 1e9 + 7;
int pa, pb;

int main() {
  INIT;
  cin >> n >> m;
  REP(i, n) {
    cin >> aa;
    a[aa] = 1;
  }
  REP(i, m) {
    cin >> bb;
    b[bb] = 1;
  }
  LL ans = 1;
  for (int i = n * m; i >= 1; i--) {
    if (!a[i] && !b[i]) {
      (ans *= pa * pb - (n * m - i)) %= mod;
    } else {
      if (a[i])
        pa++;
      if (b[i])
        pb++;
      if (a[i] && b[i])
        continue;
      else if (a[i])
        (ans *= pb) %= mod;
      else if (b[i])
        (ans *= pa) %= mod;
    }
  }
  cout << ans << endl;
}