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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;

namespace ContestCS
{
    class Program
    {
        static BigInteger Fact(BigInteger x)
        {
            BigInteger i = 1;
            for (BigInteger tmp = 1; tmp <= x; tmp++)
            {
                i *= tmp;
            }
            return i;
        }
        static void Main()
        {
            BigInteger MOD = 1000000007;
            var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int h = input[0], w = input[1], a = input[2], b = input[3];
            BigInteger[] v = new BigInteger[h - a];
            v[0] = 1;
            for (int i = 1; i < h - a; i++)
            {
                v[i] = v[i - 1] * (i + b - 1) / i;
            };
            BigInteger tmp = Fact(a + w - b - 1) / Fact(a) / Fact(w - b - 1);
            BigInteger ans = tmp * v[h - a - 1];
            for (int i = 1; i < h - a; i++)
            {
                tmp = tmp * (a + i + w - b - 1) / (a + i);
                ans += tmp * v[h - a - 1 - i];
            }
            Console.WriteLine(ans % MOD);
            Console.ReadKey();
        }
    }
}