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: Accepted)

#include<stdio.h>
#define ll long long
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
ll pom(ll a,ll n,int m){ll x=1;for(a%=m;n;n/=2)n&1?x=x*a%m:0,a=a*a%m;return x;}
#define invp(a,p)pom(a,p-2,p)
#define P 1000000007
ll fact[200010];

ll choose(n,r){
	return fact[n]*invp(fact[r]*fact[n-r],P)%P;
}

int main(){
	int h,w,a,b;
	scanf("%d%d%d%d",&h,&w,&a,&b);
	fact[0]=1;
	rep(i,1,200005)fact[i]=fact[i-1]*i%P;
	ll x=b-1,y=h-a;
	ll ans=0;
	while(x<w-1&&y>0){
		x++,y--;
		ans=(ans+choose(x+y,y)*choose((w-1-x)+(h-1-y),(h-1-y)))%P;
	}
	printf("%lld\n",ans);
	return 0;
}