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;

namespace ABC042_D
{
    class Program
    {      
        static void Main(string[] args)
        {
            var a = scan();
            maketable(a[0], a[1]);
            long ans = 0;
            for (long i =a[3]; i < a[1]; i++)
            {
                long ue = getC(a[0] - a[2] - 1, i);
                long shita = getC(a[2]-1,a[1]-i-1);             
                ans += ue * shita;
                ans %= q;
            }
            Console.WriteLine(ans);
        }

        const int q = 1000000007;
        static long[] t = new long[200000];
        static long[] s = new long[200000];

        
        //(a+b)!/a!b!｛a+bCa｝を計算
        static long getC(long a,long b)
        {
            return(((t[a+b]*s[a])% q)*s[b])%q;           
        }
        
        // x! と(x!)^-1をtableにしたいです。
        static void maketable(long H,long W)
        {
            t[0] = 1;
            s[0] = 1;
            t[1] = 1;
            s[1] = 1;
            for (long i = 2; i < H+W-1; i++)
            {
                t[i] = i*t[i - 1];
                t[i] %= q;         
            }
            s[H + W - 2] = powmod(t[H + W - 2],q-2, q);
            for (long i = H+W-2 ; i > 2; i--)
            {
                s[i-1] = (s[i] * (i)) % q;
            }
        }
       
        //a^b(modq)
        static long powmod(long a, long b, long p)
        {
            if (b == 0) return 1;
            if (b % 2 == 0)
            {
                long d = powmod(a, b / 2, p);
                return (d * d) % p;
            }
            else return (a * powmod(a, b - 1, p)) % p;         
        }

        static long[] scan()
        {
            return
               Console.ReadLine().Split(' ')
               .Select(i => long.Parse(i)).ToArray();
        }
    }

}