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)

//Problem D
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long [][] ways = new long[2][1000001];
		int height = sc.nextInt();
		int width = sc.nextInt();
		int low_l = sc.nextInt();
		int left_l = sc.nextInt();
		
		ways[0][1] = 1;
		
		for(int r = 1; r <= height; r++) {
			int c;
			if (r > height - low_l) {
				c = left_l + 1;
				ways[1][left_l] = 0;
 			} else {
 				c = 1; 
 			}
			int ll = c;
			for(;c <= width; c++) {

				ways[1][c] = ways[0][c] + ways[1][c - 1]; 
			
				while (ways[1][c] > 1000000007) {
					ways[1][c] -= 1000000007;
				}
			}
			for(int i = ll; i <= width; i++) {
				ways[0][i] = ways[1][i];
			}
		}
		System.out.println(ways[1][width]);
	}
}