Problem p02782 (C++)

Buggy submission (status: Runtime Error):
#pragma region

#include "bits/stdc++.h"
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define _rep3(i, begin, end)                                                   \
  for (register int i = (begin), i##_end = (end); i < i##_end; i++)
#define _irep3(i, begin, end)                                                  \
  for (register int i = (end)-1, i##_begin = (begin); i >= i##_begin; i--)
#define _rep2(i, n) _rep3(i, 0, n)
#define _irep2(i, n) _irep3(i, 0, n)
#define _overload3(_1, _2, _3, name, ...) name
#define rep(...) _overload3(__VA_ARGS__, _rep3, _rep2, )(__VA_ARGS__)
#define irep(...) _overload3(__VA_ARGS__, _irep3, _irep2, )(__VA_ARGS__)
#define out(x) cout << (x) << '\n';
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (line: " << __LINE__ << ") " << endl;

using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &pair) {
  cin >> pair.first >> pair.second;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "[ ";
  rep(i, vec.size()) i == 0 ? os << vec[i] : os << ", " << vec[i];
  os << " ]";
  return os;
}

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

void init() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10) << boolalpha;
}

#pragma endregion

#define MOD 1000000007
#define INF 2147483647

const int MAX = 1000010;
long long fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

long long COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main() {
  init();

  COMinit();

  int r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;

  ll ans = COM(r2 + c2 + 2, c2 + 1) - COM(r1 + c2 + 1, c2 + 1) -
           COM(r2 + c1 + 1, c1) + COM(r1 + c1, c1);

  out((ans + MOD) % MOD);
}


Fixed submission:
#pragma region

#include "bits/stdc++.h"
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define _rep3(i, begin, end)                                                   \
  for (register int i = (begin), i##_end = (end); i < i##_end; i++)
#define _irep3(i, begin, end)                                                  \
  for (register int i = (end)-1, i##_begin = (begin); i >= i##_begin; i--)
#define _rep2(i, n) _rep3(i, 0, n)
#define _irep2(i, n) _irep3(i, 0, n)
#define _overload3(_1, _2, _3, name, ...) name
#define rep(...) _overload3(__VA_ARGS__, _rep3, _rep2, )(__VA_ARGS__)
#define irep(...) _overload3(__VA_ARGS__, _irep3, _irep2, )(__VA_ARGS__)
#define out(x) cout << (x) << '\n';
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (line: " << __LINE__ << ") " << endl;

using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &pair) {
  cin >> pair.first >> pair.second;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "[ ";
  rep(i, vec.size()) i == 0 ? os << vec[i] : os << ", " << vec[i];
  os << " ]";
  return os;
}

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

void init() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10) << boolalpha;
}

#pragma endregion

#define MOD 1000000007
#define INF 2147483647

const int MAX = 2000010;
long long fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

long long COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main() {
  init();

  COMinit();

  int r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;

  ll ans = COM(r2 + c2 + 2, c2 + 1) - COM(r1 + c2 + 1, c2 + 1) -
           COM(r2 + c1 + 1, c1) + COM(r1 + c1, c1);

  out((ans + MOD) % MOD);
}