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.ArrayList;
import java.util.List;
import java.util.Scanner;

class Main {
	@SuppressWarnings("resource")
	public static void main(String args[]) {
		Scanner scanner = new Scanner(System.in);
		int h = scanner.nextInt();
		int w = scanner.nextInt();
		int a = scanner.nextInt();
		int b = scanner.nextInt();
		Coordinate start = new Coordinate(0, 0);
		Coordinate goal = new Coordinate(h - 1, w - 1);
		List<Coordinate> list = new ArrayList<>();

		for (int i = b; i <= w - 1; i++) {
			list.add(new Coordinate(h - a - 1, i));
		}

		long answer = 0;
		for (Coordinate target : list) {
			int distance1 = (target.x - start.x) + (target.y - start.y);
			int distance2 = (goal.x - (target.x + 1)) + (goal.y - target.y);
			answer += calcCombination(distance1, target.x - start.x)
					* calcCombination(distance2, goal.x - (target.x + 1));
		}

		System.out.println(answer % (int) (Math.pow(10, 9) + 7));
	}

	static long calcCombination(int n, int m) {
		if (n < m || m < 0) {
			throw new IllegalArgumentException("引数の値が不正です ( n : " + n + ", m : " + m + ")");
		}
		long c = 1;
		m = (n - m < m ? n - m : m);
		for (int ns = n - m + 1, ms = 1; ms <= m; ns++, ms++) {
			c *= ns;
			c /= ms;
		}
		return c;
	}
}

class Coordinate {
	int x;
	int y;

	Coordinate(int x, int y) {
		this.x = x;
		this.y = y;
	}

}