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<cstdio>
#include<iostream>
#include<cstring>
#define RG register
#define ll long long
using namespace std;
const int N=2e5+10;
const ll mod=1e9+7;
int n,m,a,b,maxx;
ll fac1[N]={1},inv[N]={0,1},fac2[N]={1},ans,x,y;
inline ll C(int nn,int mm){return fac1[nn]*fac2[mm]%mod*fac2[nn-mm]%mod;}
int main()
{
//	freopen("Iroha and a Grid .in","r",stdin);
	scanf("%d%d%d%d",&n,&m,&a,&b); maxx=n+m;
	for(RG int i=1;i<=maxx;i++) fac1[i]=fac1[i-1]*i%mod;
	for(RG int i=2;i<=maxx;i++) inv[i]=(mod-mod/i)*inv[mod%i]%mod;
	for(RG int i=1;i<=maxx;i++) fac2[i]=fac2[i-1]*inv[i]%mod;
	for(RG int i=1;i<=n-a;i++)
	{
		x=C(b+i-2,b-1), y=C(n+m-i-b-1,m-b-1);
		(ans+=(x*y%mod))%=mod;
	}
	printf("%lld",ans);
	return 0;
}