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: Accepted)

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    static final int MODULUS = 1_000_000_007;

    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();

        System.out.println(solve(H, W, A, B));

        sc.close();
    }

    static int solve(int H, int W, int A, int B) {
        int leftWayNum = 1;

        int rightWayNum = 1;
        for (int i = 0; i < H - 1; ++i) {
            rightWayNum = multiplyMod(rightWayNum, multiplyMod(H + W - B - 2 - i, invMod(i + 1)));
        }

        int result = 0;
        for (int i = 0; i < H - A; ++i) {
            result = addMod(result, multiplyMod(leftWayNum, rightWayNum));

            leftWayNum = multiplyMod(leftWayNum, multiplyMod(B + i, invMod(i + 1)));
            rightWayNum = multiplyMod(rightWayNum, multiplyMod(H - i - 1, invMod(H + W - B - 2 - i)));
        }

        return result;
    }

    static int invMod(int x) {
        return BigInteger.valueOf(x).modInverse(BigInteger.valueOf(MODULUS)).intValue();
    }

    static int addMod(int x, int y) {
        return (x + y) % MODULUS;
    }

    static int multiplyMod(int x, int y) {
        return (int) ((long) x * y % MODULUS);
    }
}