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.util.Scanner;

public class Main {
    private static final int MOD = 1000000007;
    private static final int MAX_N = 200005;
    private static final long[] MODULAR_INVERSE = new long[MAX_N];
    private static final long[] FACTORIAL = new long[MAX_N];

    private static long pow(long base, int exp) {
        long ret = 1;
        while (exp != 0) {
            if ((exp & 1) != 0) ret = (ret * base) % MOD;
            base = (base * base) % MOD;
            exp >>= 1;
        }
        return ret;
    }


    private static void pre(int N) {
        FACTORIAL[0] = 1;
        for (int i = 1; i < MAX_N; i++) FACTORIAL[i] = FACTORIAL[i - 1] * i % MOD;
        MODULAR_INVERSE[0] = 1;
        MODULAR_INVERSE[N] = pow(FACTORIAL[N], MOD - 2);
        for (int i = N - 1; i > 0; i--)
            MODULAR_INVERSE[i] = MODULAR_INVERSE[i + 1] * (i + 1) % MOD;
    }

    private static long binomial_coefficient(int n, int r) {
        if (n < 0 || r < 0) return 1;
        return FACTORIAL[n] * MODULAR_INVERSE[r] % MOD * MODULAR_INVERSE[n - r] % MOD;
    }

    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            int H = sc.nextInt();
            int W = sc.nextInt();
            int A = sc.nextInt();
            int B = sc.nextInt();
            pre(H + W - 2);
            long ans = 0;
            for (int i = B + 1; i <= W; i++) {
                ans += binomial_coefficient(H - A + i - 2, i - 1) * binomial_coefficient(A + W - i - 1, A - 1) % MOD;
                ans %= MOD;
            }
            System.out.println(ans);
        }
    }
}