Problem:
Score : 400 points

Problem Statement

We have a large square grid with H rows and W columns.
Iroha is now standing in the top-left cell.
She will repeat going right or down to the adjacent cell, until she reaches the bottom-right cell.

However, she cannot enter the cells in the intersection of the bottom A rows and the leftmost B columns. (That is, there are A×B forbidden cells.) There is no restriction on entering the other cells.

Find the number of ways she can travel to the bottom-right cell.

Since this number can be extremely large, print the number modulo 10^9+7.

Constraints

1 ≦ H, W ≦ 100,000

1 ≦ A < H

1 ≦ B < W

Input

The input is given from Standard Input in the following format:

H W A B

Output

Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7.

Sample Input 1

2 3 1 1

Sample Output 1

2

We have a 2×3 grid, but entering the bottom-left cell is forbidden. The number of ways to travel is two: "Right, Right, Down" and "Right, Down, Right".

Sample Input 2

10 7 3 4

Sample Output 2

3570

There are 12 forbidden cells.

Sample Input 3

100000 100000 99999 99999

Sample Output 3

1

Sample Input 4

100000 100000 44444 55555

Sample Output 4

738162020

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
constexpr int64_t MOD = 1e9 + 7;
constexpr int64_t SIZE = 2e5;

array<int64_t, SIZE+10> fac, ifac;

int64_t modpow(int64_t x, int64_t n, int64_t m = 1) {
    return n == 0 ? m : modpow(x * x % MOD, n >> 1, n & 1 ? m * x % MOD : m);
}

int64_t comb(int64_t n, int64_t k) {
    return n == 0 && k == 0 ? 1
        : n < k || n < 0 ? 0
        : fac[n] * ifac[k] % MOD * ifac[n-k] % MOD;
}

int main() {
    fac[0] = ifac[0] = 1;
    for (int64_t i = 0; i+1 < SIZE + 10; i++) {
        fac[i+1] = fac[i] * (i+1) % MOD;
        ifac[i+1] = ifac[i] * modpow(i+1, MOD-2) % MOD;
    }

    int64_t h, w, a, b;
    cin >> h >> w >> a >> b;

    int64_t ans = 0;
    for (int i = 0; i < h-a; i++) {
        ans += comb(i+b-1, i) * comb(h-1-i + w-b-1, w-b-1) % MOD;
        ans %= MOD;
    }

    cout << ans << endl;
}