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>
#define ri register int
using namespace std;
typedef long long ll;
const int N=2e5+5,mod=1e9+7;
int h,w,a,b,fac[N],ifac[N],ans=0,up;
inline int C(int n,int m){return (ll)fac[n]*ifac[m]%mod*ifac[n-m]%mod;}
int main(){
	scanf("%d%d%d%d",&h,&w,&a,&b),up=max(w,h),fac[0]=fac[1]=ifac[0]=ifac[1]=1;
	for(ri i=2;i<=up<<1;++i)fac[i]=(ll)fac[i-1]*i%mod,ifac[i]=(ll)ifac[mod%i]*(mod-mod/i)%mod;
	for(ri i=2;i<=up<<1;++i)ifac[i]=(ll)ifac[i]*ifac[i-1]%mod;
	for(ri i=1;i<=h-a;++i)(ans+=(ll)C(b+i-2,b-1)*C(h+w-b-i-1,w-b-1)%mod)%=mod;
	cout<<ans;
	return 0;
}