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;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;

class Magatro
{
    static int H, W, A, B;
    const int MOD = 1000000007;
    static long[] x;
    static long[] xx;
    static void Main()
    {
        string[] s = Console.ReadLine().Split(' ');
        H = int.Parse(s[0]);
        W = int.Parse(s[1]);
        A = int.Parse(s[2]);
        B = int.Parse(s[3]);
         x = new long[H + W - 1];
        xx = new long[H + W - 1];
        x[0] = 1;
        xx[0] = 1;
        for(int i = 1; i <= H + W - 2; i++)
        {
            x[i] = (x[i - 1] * i) % MOD;
            xx[i] = Pow(x[i], MOD - 2);
        }
        long cnt = 0;
        for(int i = B; i < W; i++)
        {
            long a = nCm(H-A-1+i,i);
            a = (a * nCm(W-1-i+A-1 , A-1)) % MOD;
            cnt = (cnt + a) % MOD;
        }
        Console.WriteLine(cnt);
    }
    static long nCm(int n,int m)
    {
        long a = (x[n] * xx[m]) % MOD;
        return (a * xx[n - m]) % MOD;
    }
    static long Pow(long x, long y)
    {
        long r = 1;
        long p = x % MOD;
        while (y > 0)
        {
            if (y % 2 == 0)
            {
                p = (p * p) % MOD;
                y /= 2;
            }
            else
            {
                r = (r * p) % MOD;
                y--;
            }

        }
        return r;
    }
}