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: Memory Limit Exceeded)

import java.util.*;

public class Main {

    public static void main(String[] args) {
       Scanner scan=new Scanner(System.in);

        int h=scan.nextInt();
        int w=scan.nextInt();
        int a=scan.nextInt();
        int b=scan.nextInt();
        long [][]map=new long [h+1][w+1];

        long waru=1000000007;


        for(int i=h-1;i>=0;i--){
            for(int j=w-1;j>=0;j--){
                if(i==h-1 &&j==w-1)
                    map[i][j]=1;
                else
                    map[i][j]=(map[i][j+1]+map[i+1][j])%waru;

                if(j<=b-1 && i>=h-a)
                    map[i][j]=0;
            }
        }

        System.out.println(map[0][0]);
    }
}