Problem p04046 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <string>
#include <utility>
#include <vector>
using namespace std;
using pii = pair<int, int>;
using ll = long long;
using ld = long double;
#define pb push_back
#define mp make_pair
#define stpr setprecision
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define REP(i, a, b) for (ll i = (a); i < (b); ++i)
#define crep(i) for (char i = 'a'; i <= 'z'; ++i)
#define psortsecond(A, N)                                                      \
  sort(A, A + N,                                                               \
       [](const pii &a, const pii &b) { return a.second < b.second; });
#define ALL(x) (x).begin(), (x).end()
#define endl '\n'
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
constexpr ll MOD = 1000000007;
constexpr ld EPS = 10e-8;
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &&x : v)
    is >> x;
  return is;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first;
  is >> p.second;
  return is;
}
template <typename T, typename U>
ostream &operator>>(ostream &os, const pair<T, U> &p) {
  os << p.first << ' ' << p.second;
  return os;
}
template <class T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (auto i = begin(v); i != end(v); ++i) {
    if (i != begin(v))
      os << ' ';
    os << *i;
  }
  return os;
}

const int MAX = 100007;

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;
  }
}

// 二項係数計算
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() {
  // 前処理
  COMinit();
  ll H, W, A, B, C = 0;
  cin >> H >> W >> A >> B;
  rep(i, H - A) {
    C += COM(i + B - 1, B - 1) * COM(W - B + H - i - 2, W - B - 1);
    C %= MOD;
  }
  cout << C << endl;
}

Fixed submission:
#include <algorithm>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <string>
#include <utility>
#include <vector>
using namespace std;
using pii = pair<int, int>;
using ll = long long;
using ld = long double;
#define pb push_back
#define mp make_pair
#define stpr setprecision
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define REP(i, a, b) for (ll i = (a); i < (b); ++i)
#define crep(i) for (char i = 'a'; i <= 'z'; ++i)
#define psortsecond(A, N)                                                      \
  sort(A, A + N,                                                               \
       [](const pii &a, const pii &b) { return a.second < b.second; });
#define ALL(x) (x).begin(), (x).end()
#define endl '\n'
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
constexpr ll MOD = 1000000007;
constexpr ld EPS = 10e-8;
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &&x : v)
    is >> x;
  return is;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first;
  is >> p.second;
  return is;
}
template <typename T, typename U>
ostream &operator>>(ostream &os, const pair<T, U> &p) {
  os << p.first << ' ' << p.second;
  return os;
}
template <class T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (auto i = begin(v); i != end(v); ++i) {
    if (i != begin(v))
      os << ' ';
    os << *i;
  }
  return os;
}

const int MAX = 510000;

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;
  }
}

// 二項係数計算
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() {
  // 前処理
  COMinit();
  ll H, W, A, B, C = 0;
  cin >> H >> W >> A >> B;
  rep(i, H - A) {
    C += COM(i + B - 1, B - 1) * COM(W - B + H - i - 2, W - B - 1);
    C %= MOD;
  }
  cout << C << endl;
}