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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.Scanner;
public class Main {
	public static BigInteger fact(int x)
	{	BigInteger re = new BigInteger("1");
		if(x==0)
			return new BigInteger("1");
		for(int i=1;i<=x;i++)
			re= re.multiply(new BigInteger(Integer.toString(i)));
		return re;
	}
	public static BigInteger combine(int n, int r)
	{
		BigInteger posi;
		posi = fact(n+r).divide(fact(n).multiply(fact(r)));
		return posi;
		
	}
	public static void main(String[] args)
	{	
		
		
			int h,w;
			int a,b;
			Scanner sc = new Scanner(System.in);
			h = sc.nextInt();
			w = sc.nextInt();
			a = sc.nextInt();
			b = sc.nextInt();
			BigInteger sum = new BigInteger("0");
			sum = sum.add(combine(w-b-1,h-1));
			
			for(int i=2;i<=(h-a);i++)
			{	
				BigInteger n = combine(b-1,i-1);
				sum = sum.add(n.multiply(combine(w-b-1,h-i)));
				
			}
			BigInteger modulo= new BigInteger(Integer.toString(1000000007));
			sum = sum.mod(modulo);
			System.out.println(sum);
		
	}
	
}