Problem p02782 (C++)

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

using namespace std;

using ll = long long;
using P = pair<ll, ll>;
using Graph = vector<vector<ll>>;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rep2(i, m, n) for (ll i = m; i < (ll)(n); i++)
#define rrep(i, n, m) for (ll i = n; i >= (ll)(m); i--)
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
const int ddx[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const int ddy[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const ll MOD = 1000000007;
const ll INF = 1000000000000000000L;
#ifdef __DEBUG

/**
 * For DEBUG
 * https://github.com/ta7uw/cpp-pyprint
 */
#include "cpp-pyprint/pyprint.h"

#endif

const int MAX = 1010000;
long long fac[MAX], finv[MAX], inv[MAX];
bool initialized = false;

/**
 * @fn
 * This function must be called at first.
 */
void combination_init() {
  initialized = true;
  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;
  }
}

/**
 * @fn
 * Calculates the combination  ( nCK % p: N choose K mod p).
 *
 * @brief constraint: 1 ≤ k ≤ n ≤ 10^7
 * @return nCK % MOD
 */
long long combination(int n, int k) {
  assert(initialized);
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

/**
 * @fn
 * Calculates the factorial of the number.
 *
 * @return N! % MOD
 */
long long factorial(int n) {
  assert(initialized);
  if (n < 0)
    return 0;
  return fac[n] % MOD;
}

/**
 * @fn
 * Calculates the combination ( nCK % p: N choose K mod p).
 *
 * @brief constraint: 1 ≤ k ≤ 10^7 and 1 ≤ n ≤ 10^9
 * @return nCK % MOD
 */
long long combination2(int n, int k) {
  assert(initialized);
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  ll res = 1;
  k = min(k, n - k);
  for (long long x = 1; x <= k; x++) {
    res *= (n - x + 1);
    res %= MOD;
    res *= inv[x];
    res %= MOD;
  }
  return res;
}

ll f(ll r, ll c) { return combination(r + c + 2, r + 1) - 1; }

void Main() {
  ll r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;
  combination_init();
  ll ans = f(r2, c2);
  ans %= MOD;
  ans -= f(r2, c1 - 1);
  ans %= MOD;
  if (ans < 0)
    ans += MOD;
  ans -= f(r1 - 1, c2);
  ans %= MOD;
  if (ans < 0)
    ans += MOD;
  ans += f(r1 - 1, c1 - 1);
  ans %= MOD;
  cout << ans << '\n';
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}


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

using namespace std;

using ll = long long;
using P = pair<ll, ll>;
using Graph = vector<vector<ll>>;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rep2(i, m, n) for (ll i = m; i < (ll)(n); i++)
#define rrep(i, n, m) for (ll i = n; i >= (ll)(m); i--)
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
const int ddx[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const int ddy[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const ll MOD = 1000000007;
const ll INF = 1000000000000000000L;
#ifdef __DEBUG

/**
 * For DEBUG
 * https://github.com/ta7uw/cpp-pyprint
 */
#include "cpp-pyprint/pyprint.h"

#endif

const int MAX = 3010000;
long long fac[MAX], finv[MAX], inv[MAX];
bool initialized = false;

/**
 * @fn
 * This function must be called at first.
 */
void combination_init() {
  initialized = true;
  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;
  }
}

/**
 * @fn
 * Calculates the combination  ( nCK % p: N choose K mod p).
 *
 * @brief constraint: 1 ≤ k ≤ n ≤ 10^7
 * @return nCK % MOD
 */
long long combination(int n, int k) {
  assert(initialized);
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

/**
 * @fn
 * Calculates the factorial of the number.
 *
 * @return N! % MOD
 */
long long factorial(int n) {
  assert(initialized);
  if (n < 0)
    return 0;
  return fac[n] % MOD;
}

/**
 * @fn
 * Calculates the combination ( nCK % p: N choose K mod p).
 *
 * @brief constraint: 1 ≤ k ≤ 10^7 and 1 ≤ n ≤ 10^9
 * @return nCK % MOD
 */
long long combination2(int n, int k) {
  assert(initialized);
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  ll res = 1;
  k = min(k, n - k);
  for (long long x = 1; x <= k; x++) {
    res *= (n - x + 1);
    res %= MOD;
    res *= inv[x];
    res %= MOD;
  }
  return res;
}

ll f(ll r, ll c) { return combination(r + c + 2, r + 1) - 1; }

void Main() {
  ll r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;
  combination_init();
  ll ans = f(r2, c2);
  ans %= MOD;
  ans -= f(r2, c1 - 1);
  ans %= MOD;
  if (ans < 0)
    ans += MOD;
  ans -= f(r1 - 1, c2);
  ans %= MOD;
  if (ans < 0)
    ans += MOD;
  ans += f(r1 - 1, c1 - 1);
  ans %= MOD;
  cout << ans << '\n';
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  Main();
  return 0;
}