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 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>

int main(){
	long long h,w,a,b,ans=0,s,k;
	long long x[1000][100],y[100][100];
	
	scanf("%lld%lld%lld%lld",&h,&w,&a,&b);
	
	for(int i=1;i<=h;i++){
		x[i][1]=1;
		y[i][1]=1;
	}
	for(int j=1;j<=w;j++){
		x[1][j]=1;
		y[1][j]=1;
	}
	
	for(int i=2;i<=h-a;i++){
		for(int j=2;j<=b;j++){
			x[i][j]=x[i][j-1]+x[i-1][j];
		}
	}
	
	for(int i=2;i<=h;i++){
		for(int j=2;j<=w-b;j++){
			y[i][j]=y[i][j-1]+y[i-1][j];
		}
	}

//	printf("%lld",x[3][10]);
	for(k=h-a,s=a+1;k>0;k--,s++){
		ans+=x[k][b]*y[s][w-b];
	}
	printf("%lld",ans);
	return 0;
}