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>
using namespace std;
typedef long long ll;
const int N=2e5+10,p=1e9+7;
int inc(int x,int y){x+=y;return x>=p?x-p:x;}
int mul(int x,int y){return (ll)x*y%p;}
int power(int x,int y){
	int ans=1;
	for (;y;y>>=1,x=mul(x,x))
		if (y&1) ans=mul(ans,x);
	return ans;
}
int n,m,a,b,fac[N],ifac[N];
int C(int n,int m){
	return mul(fac[n],mul(ifac[m],ifac[n-m]));
}
int main()
{
	cin>>n>>m>>a>>b;
	fac[0]=1;
	for (int i=1;i<N;i++) fac[i]=mul(fac[i-1],i);
	ifac[N-1]=power(fac[N-1],p-2);
	for (int i=N-1;i;i--) ifac[i-1]=mul(ifac[i],i);
	int ans=0;
	for (int i=b+1;i<=m;i++) ans=inc(ans,mul(C(n-a+i-2,n-a-1),C(a-1+m-i,a-1)));
	cout<<ans<<endl;
	return 0;
}