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: Runtime Error)

using System;

class quiz
{
    public long solve(int H, int W, int A, int B)
    {
        long ans = 0;
        long[] fac = new long[H - 1 + W - 1 + 1];

        for (int i = 0; i < fac.Length; i++)
        {
            fac[i] = Factorial(i);
        }

        ans = fac[H - 1 + W - 1] / (fac[W - 1] * fac[H - 1]);

        for (int i = 0; i < A; i++)
        {
            ans -= (fac[B - 1 + H - A + i] / (fac[B - 1] * fac[H - A + i])) * (fac[W - B - 1 + A - i - 1] / (fac[W - B - 1] * fac[A - i - 1]));
        }

        return (long)ans % 1000000007;
    }

    long Factorial(int n)
    {
        if (n == 0)
            return 1;

        return n * Factorial(n - 1);
    }

    public int[] ParseIntBySpace(string str)
    {
        int[] array = new int[str.Length];
        int lastloc = 0, spaceloc = -1;

        for (int i = 0; i < str.Length; i++)
        {
            if (str[i] == ' ')
            {
                array[lastloc++] = int.Parse(str.Substring(spaceloc + 1, i - spaceloc - 1));
                spaceloc = i;
            }
            else if (i == str.Length - 1)
            {
                array[lastloc++] = int.Parse(str.Substring(spaceloc + 1, i - spaceloc));
            }
        }

        Array.Resize(ref array, lastloc);

        return array;
    }
}

class Example
{
    static void Main()
    {
        quiz ex = new quiz();

        int[] HWAB = ex.ParseIntBySpace(Console.ReadLine());

        Console.WriteLine(ex.solve(HWAB[0],HWAB[1],HWAB[2],HWAB[3]));
    }
}