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;
const int mod=1e9+7;
typedef long long ll;
const int N=200000;
ll fac[N+5],inv[N+5];
int h,w,a,b;
ll fast_pow(int a,int b)
{
	ll res=1,tmp=a;
	for(;b;tmp=tmp*tmp%mod,b>>=1)
		if(b&1) res=res*tmp%mod;
	return res;
}
ll work(int n,int m)
{
	return fac[n]*inv[m]%mod*inv[n-m]%mod;
}
int main()
{
	fac[0]=1;for(int i=1;i<=N;++i) fac[i]=fac[i-1]*i%mod;
	
	inv[N]=fast_pow(fac[N],mod-2);
	for(int i=N-1;i>=0;--i)
	inv[i]=(i+1)*inv[i+1]%mod;
	scanf("%d%d%d%d",&h,&w,&a,&b);
	a=h-a;b++;
	ll ans=0;
	for(int i=1;i<=a;++i) ans=(ans+work(b+i-3,b-2)*work(h-i+w-b,h-i)%mod)%mod;
	cout<<ans;
}