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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
class Program{
	const int mod=1000000007;
	static void Main(){
		int[] s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		long[] fo=new long[s[0]+s[1]-1];
		long[] a=new long[s[1]-s[3]];
		long[] b=new long[s[1]-s[3]];
		fo[0]=1;a[0]=1;b[0]=1;
		for(int i=1;i<=s[0]+s[1]-2-s[2];i++){
			fo[i]=(fo[i-1]*i)%mod;
			if(i>=s[0]+s[3]-1-s[2]&&i<=s[0]+s[1]-2-s[2]){a[i-(s[0]+s[3]-1-s[2])]=fo[i];}
			if(i>=s[2]-1&&i<s[2]+(s[1]-s[3])-1){b[(i-s[2]+1)]=fo[i];}
		}
		for(int i=0;i<s[1]-s[3];i++){
			a[i]=(a[i]*(mi(fo[s[0]-1-s[2]]*fo[s[3]+i])%mod))%mod;
			b[i]=(b[i]*(mi(fo[s[2]-1]*fo[i])%mod))%mod;
		}
		long ans=0;
		for(int i=0;i<s[1]-s[3];i++){ans=(ans+a[i]*b[s[1]-s[3]-i-1])%mod;}
		Console.WriteLine(ans);
	}
	static long mi(long a){
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;a^=b;b^=a;a^=b;
			u-=t*v;u^=v;v^=u;u^=v;
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}