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.Scanner;

class Main {
    static final long mod = 1000000000 + 7;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int h = sc.nextInt();
        int w = sc.nextInt();
        int a = sc.nextInt();
        int b = sc.nextInt();
        sc.close();
        long[] ans = new long[w];
        for (int j = 0; j < w; j++) {
            ans[j] = 1;
            if (j < b) {

            }
        }
        for (int i = 1; i < h; i++) {
            for (int j = 0; j < w; j++) {
                if (i >= h - a && j <= b - 1) {
                    ans[j] = 0;
                } else {

                    if (j == 0) {
                        ans[j] = ans[j];
                    } else {
                        ans[j] = (ans[j] + ans[j - 1]) % mod;
                    }
                }
            }
        }

        System.out.println(ans[w - 1]);
    }
}