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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class ABC058 {
    static void Main(string[] args) {
        var spl = Console.ReadLine().Split();
        long H = long.Parse(spl[0]);
        long W = long.Parse(spl[1]);
        long A = long.Parse(spl[2]);
        long B = long.Parse(spl[3]);

        long res = 0;
        //for(long i = 0; i < H - A; i++) {
        //    long total = H - i + W - B - 2;
        //    long right = comb(total, H - i - 1);
        //    total = B + i + 1 - 2;
        //    long left = comb(total, i);
        //    long prod = (left * right) % 1000000007;
        //    res = (res + prod) % 1000000007;
        //}

        var right = new long[H + 1];
        for (long i = H - A - 1; i >= 0; i--) {
            long total = H - i + W - B - 2;
            right[i] = (i == H - A - 1) ? comb(total, H - i - 1) : ((right[i + 1] * (total / (H - i - 1))) % 1000000007);
        }

        long left = -1;
        for (long i = 0; i < H - A; i++) {
            long total = B + i + 1 - 2;
            left = left == -1 ? comb(total, i) : ((left * (total / i)) % 1000000007);
            long prod = (left * right[i]) % 1000000007;
            res = (res + prod) % 1000000007;
        }

        //var left = new long[H + 1];
        //for (long i = 0; i < H - A; i++) {
        //    long total = B - 1 + i;
        //    left[i] = i == 0 ? 1 : (left[i - 1] * total / i) % 1000000007;
        //}

        //long right = -1;
        //for (long i = H - A - 1; i >= 0; i--) {
        //    long total = W - B + H - i - 2;
        //    right = i == H - A - 1 ? comb(total, H - i - 1) : (right * total / (H - i - 1)) % 1000000007;
        //    res += left[i] * right;
        //}


        Console.WriteLine(res.ToString());
    }

    private static long comb(long n, long r) {
        r = Math.Min(r, n - r);
        if (r < 0) return 0;
        long ret = 1;
        for (long i = 1; i <= r; i++) {
            ret = (ret * (n + 1 - i) / i) % 1000000007;
        }
        return ret;
    }
}