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.Arrays;
import java.util.Scanner;

public class Main {

	private long INF = 1_000_000_000 + 7;

	void run() {
		Scanner sc = new Scanner(System.in);

		int h = sc.nextInt();
		int w = sc.nextInt();

		long[][] grid = new long[h][w];
		boolean[][] pass = new boolean[h][w];
		for (int i = 0; i < h; i++) {
			Arrays.fill(pass[i], true);
		}

		int a = sc.nextInt();
		int b = sc.nextInt();

		for (int i = h - a; i < h; i++) {
			for (int j = 0; j < b; j++) {
				pass[i][j] = false;
			}
		}

		for (int i = 0; i < h; i++) {
			if (pass[i][0]) {
				grid[i][0] = 1;
			} else {
				grid[i][0] = 0;
			}
		}
		for (int j = 0; j < w; j++) {
			if (pass[0][j]) {
				grid[0][j] = 1;
			} else {
				grid[0][j] = 0;
			}
		}

		for (int i = 1; i < h; i++) {
			for (int j = 1; j < w; j++) {
				if (pass[i][j]) {
					grid[i][j] = (grid[i - 1][j] % INF + grid[i][j - 1] % INF) % INF;
				} else {
					grid[i][j] = 0;
				}
			}
		}

		System.out.println(grid[h - 1][w - 1] % INF);
	}

	public static void main(String[] args) {
		new Main().run();
	}

}