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)

import java.util.*;

public class Main {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        int h = scanner.nextInt();
        int w = scanner.nextInt();
        int a = scanner.nextInt();
        int b = scanner.nextInt();

        long ans = 0;
        for (int i = b; i < w; i++) {
            ans = (ans + f(i, h - a - 1) * f(w - i - 1, a - 1) % 1000000007) % 1000000007;
        }
        System.out.println(ans);
    }

    static long f(long h, long w) {
        return combinationAndMod(h + w, Math.min(h, w));
    }

    static long combinationAndMod(long n, long r) {
        long x = 1, y = 1;
        for (long i = 1; i <= r; i++) {
            x = x * (n - r + i) % 1000000007;
            y = y * i % 1000000007;
        }
        return x * powAndMod(y, 1000000005) % 1000000007;
    }

    static long powAndMod(long a, long b) {
        if (b == 0)
            return 1;
        if ((b & 1) == 1)
            return a * powAndMod(a, b - 1) % 1000000007;
        return powAndMod(a * a % 1000000007, b / 2);
    }
}