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: Wrong Answer)

import java.util.Scanner;

/**
 * 大岩達典 J4-170821<br>
 * D-いろはちゃんとます目<br>
 * https://beta.atcoder.jp/contests/abc042/tasks/arc058_b
 * <br>
 * 教壇から見て左中央<br>
 * <br>
 */
public class Main {
	
	public static final int MAX = 1000000007;
	public static int[] FRACTION;
	
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		
		final int height = scanner.nextInt();
		final int width = scanner.nextInt();
		final int bottom = scanner.nextInt();
		final int left = scanner.nextInt();
		scanner.close();
		initFrac(height + width);
		
		int result = 0;
		
		for (int i = left; i < width;i++) {
			result += (combination(height-bottom-1, i) * combination(bottom-1, width-i-1));
		}
		System.out.println(result);
	}
	
	public static int combination(int a, int b) {
		return fraction(a+b) / fraction(a) / fraction(b);
	}
	
	public static int fraction(int a) {
		return FRACTION[a];
	}
	
	public static void initFrac(int max) {
		FRACTION = new int[max];
		long prev = 1;
		FRACTION[0] = (int)prev;
		for (int i = 1; i < FRACTION.length; i++) {
			prev = (prev*i)%MAX;
			FRACTION[i] = (int)(prev % MAX);
		}
	}
}