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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
const long long int MOD = 1e9 + 7;
long long int h,w,a,b;
long long permutation(long long int x, long long int y){
	if(x >= h or y >= w) return 1;
	if(x<a-1 or y<b-1){
		if(x<a-1 and y<b-1) return (2*permutation(x+1,y))%MOD*(permutation(x,y+1))%MOD;
		else if(x<a-1 and y>=b-1) return 1*permutation(x+1,y)%MOD;
		else return 1*permutation(x,y+1)%MOD;
	} else{
		if(x<h-1 and y<w-1) return (2*permutation(x+1,y))%MOD*(permutation(x,y+1))%MOD;
		else if(x<h-1 and y>=w-1) return 1*permutation(x+1,y)%MOD;
		else return 1*permutation(x,y+1)%MOD;
	}
}

int main()
{
	//ios::sync_with_stdio(0),cin.tie(0);
	scanf("%lld %lld %lld %lld",&h, &w, &a, &b);
	long long answer = permutation(1,1);
	printf("%lld\n",answer);

}