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

namespace CompetitiveProgramming
{

  class Solve 
  {
    const int MOD = (int)(1e9) + 7;
    public Solve() 
    {
      ulong[] input = Console.ReadLine().Split().Select(ulong.Parse).ToArray();
      ulong H = input[0];
      ulong W = input[1];
      ulong A = input[2];
      ulong B = input[3];


      ulong[,] t = new ulong[H + W + 1, 2];

      t[0, 0] = 1;
      for (ulong i = 0; i <= H + W; i++)
      {
        ulong f = 1;
        if (i > 0)
        {
          f = (t[i - 1, 0] * i) % MOD;
        }
        ulong g = MyMath.ModExpo(f, MOD - 2, MOD);
        t[i, 0] = f;
        t[i, 1] = g;
      }
      

      ulong ans = 0;
      for (ulong i = B; i < W; i++)
      {
        ulong u, v, w;
      
        u = H - A - 1 + i;
        v = (((t[u, 0] * t[i, 1]) % MOD) * t[u - i, 1]) % MOD;

        u = H - 1 - (H - A) + (W - i - 1);
        w = (((t[u, 0] * t[A - 1, 1]) % MOD) * t[u - (A - 1), 1]) % MOD;

        ans = (ans + v * w) % MOD;
      }

      Console.WriteLine(ans);
    }
  }
  class Program
  {
    static void Main(string[] args)
    {
      new Solve();
    }
  }
  
  class MyMath
  {
    public static ulong ModExpo(ulong n, ulong r, ulong mod) 
    {
      if (r == 0)
      {
        return 1;
      }
      if (r == 1)
      {
        return n % mod;
      }
      ulong a = ModExpo(n, r / 2, mod);
      if (r % 2 == 0)
      {
        return ((a % mod) * (a % mod)) % mod;
      }
      else 
      {
        return ((((n % mod) * (a % mod)) % mod) * (a % mod)) % mod;
      }
    }

    public static ulong ModFact(ulong n, ulong mod)
    {
      ulong ret = 1;
      for (ulong i = 1; i < n; i++)
      {
        ret = (ret * n) % mod;
      }

      return ret;
    }
  }

}