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.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int h=sc.nextInt();
		int w=sc.nextInt();
		int a=sc.nextInt();
		int b=sc.nextInt();
		int sr=h-a;
		int ec=b-1;
		long mod=1000000007;
	  long ar[][]=new long[h][w];
		ar[h-1][w-1]=1;
		for(int i=h-1;i>=0;i--)
		{
			for(int j=w-1;j>=0;j--)
			{
				if(i>=sr&&j<=ec)
				continue;
				if((i+1<sr||j>ec)&&i+1<h)
				ar[i][j]+=ar[i+1][j]%mod;
				int j1=j+1;
				if((i<sr||j1>ec)&&j1<w)
				ar[i][j]+=ar[i][j1]%mod;
				ar[i][j]%=mod;
			}
		}
		System.out.println(ar[0][0]);
	}
}