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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        D solver = new D();
        solver.solve(1, in, out);
        out.close();
    }

    static class D {
        int H;
        int W;
        int A;
        int B;
        int MOD = (int) 1e9 + 7;
        private static int MAX = 200000;
        private static long[] xs = new long[MAX + 1];
        private static long[] ys = new long[MAX + 1];

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            H = in.nextInt();
            W = in.nextInt();
            A = in.nextInt();
            B = in.nextInt();

            long ans = 0;
            for (int i = B; i < W; i++) {
                long x1 = comb(i + H - A - 1, i);
                long x2 = comb(W - i - 1 + A - 1, W - i - 1);
                ans += x1 * x2 % MOD;
                ans %= MOD;
            }
            out.println(ans);
        }

        private long comb(int n, int r) {
            if (r < 0 || r > n) return 0;
            if (xs[0] == 0) {
                xs[0] = 1;
                for (int i = 1; i <= MAX; i++) {
                    xs[i] = xs[i - 1] * i % MOD;
                }
                long inv = modpow(xs[MAX]);
                ys[MAX] = inv;
                for (int i = MAX; i >= 1; i--) {
                    inv = inv * i % MOD;
                    ys[i - 1] = inv;
                }
            }
            return xs[n] * (ys[r] * ys[n - r] % MOD) % MOD;
        }

        private long modpow(long a) {
            return modpow(a, MOD - 2);
        }

        private long modpow(long a, long n) {
            long r = 1;
            while (n > 0) {
                r = r * ((n % 2) != 0 ? a : 1) % MOD;
                a = a * a % MOD;
                n >>= 1;
            }
            return r;
        }

    }
}