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: Accepted)

using System;

public class Hello
{
    const int MOD = 1000000007;
    const int FMAX = 510000;
    public static void Main()
    {
        var fac = new long[FMAX];
        var finv = new long[FMAX];
        var inv = new long[FMAX];
        COMinit(fac, finv, inv);
        string[] line = Console.ReadLine().Trim().Split(' ');
        var h = int.Parse(line[0]);
        var w = int.Parse(line[1]);
        var a = int.Parse(line[2]);
        var b = int.Parse(line[3]);
        var ha1 = h - a - 1;
        var imax = w - b;
        var ret = 0L;
        for (int i = 0; i < imax; i++)
        {
            var ww1 = ha1 + b + i;
            var ww2 = a - 2 + imax - i;
            ret += (COM(fac, finv, inv, ww1, ha1) * COM(fac, finv, inv, ww2, a - 1)) % MOD;
            ret %= MOD;
        }
        Console.WriteLine(ret);
    }
    public static long COM(long[] fac, long[] finv, long[] inv, int n, int k)
    {
        if (n < k) return 0;
        if (n < 0 | k < 0) return 0;
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }
    public static void COMinit(long[] fac, long[] finv, long[] inv)
    {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for (int i = 2; i < FMAX; i++)
        {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
}