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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int h,w,a,b;
const int N=200010;
int fac[N],inv[N];
const int mod=1000000007;
int qp(int x,int k)
{
	int res=1;
	while(k)
	{
		if(k&1)res=1ll*res*x%mod;
		x=1ll*x*x%mod;
		k>>=1;
	}
	return res;
}
void init()
{
	fac[0]=inv[0]=1;
	for(int i=1;i<N;i++)
		fac[i]=1ll*fac[i-1]*i%mod;
	inv[N-1]=qp(fac[N-1],mod-2);
	for(int i=N-2;i>=1;i--)
		inv[i]=1ll*inv[i+1]*(i+1)%mod;
}
int C(int a,int b)
{
	if(a<b)return 0;
	return 1ll*fac[a]*inv[b]%mod*inv[a-b]%mod;
}
int ans;
int main()
{
	init();
	scanf("%d%d%d%d",&h,&w,&a,&b);
	ans=C(h-1+w-1,h-1);
	for(int i=1;i<=min(a,b);i++)
		ans=(ans-1ll*C(h-a+b-1,b-i)*C(w-b+a-1,a-i)+mod)%mod;
	printf("%d\n",ans);
	return 0;
}