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;


class NumberTheory {
    bool isFact;
    long[] fact;
    public NumberTheory(){
        isFact = false;
    }
    
    public void FactTable(long n, long m){
        isFact = true;
        fact = new long[n+1];
        fact[0] = 1;
        for(long i=1;i<n+1;i++){
            fact[i] = (fact[i-1]*i)%m;
        }
    }
    
    public long GetFact(long n){
        if(isFact && -1<n && n<=fact.Length){
            return fact[n];
        } else {
            return -1;
        }
    }
    
    public long Mod_fact(long n, long p, out long e){
        e = 0;
        if(!isFact){
            Console.WriteLine("Error:FactTable is not created!!");
            return -1;
        }
        if(n==0) return 1;
        long res = Mod_fact(n/p,p, out e);
        e += n/p;
        
        if(n/p%2!=0) return res * (p-fact[n%p])%p;
        return res*fact[n%p]%p;
    }
    
    public long Mod_cmb(long n, long k, long p){
        if(n<0||k<0||n<k) return 0;
        long e1,e2,e3;
        long a1 = Mod_fact(n,p, out e1),a2 = Mod_fact(k,p, out e2),a3 = Mod_fact(n-k,p, out e3);
        if(e1>e2+e3) return 0;
        return a1 * Mod_inverse(a2*a3%p, p)%p;
    }
    
    public long Extgcd(long a, long b, out long x, out long y){
        long d = a;
        if(b!=0){
            d = Extgcd(b,a%b, out y, out x);
            y -= (a/b)*x;
        } else {
            x = 1; y = 0;
        }
        return d;
    }
    
    public long Mod_inverse(long a, long m){
        long x,y;
        Extgcd(a,m, out x, out y);
        return (m+x%m)%m;
    }
    
}

public class Program{
    static void Main(string[] args){
        long N = 1000000007;
        NumberTheory nt = new  NumberTheory();
        string[]  str = Console.ReadLine().Split(' ');
        long H = long.Parse(str[0]);
        long W = long.Parse(str[1]);
        nt.FactTable(H+W,N);
        long A = long.Parse(str[2]);
        long B = long.Parse(str[3]);
        long ans = 0;
        for(int i=1;i<H-A+1;i++){
            ans +=  nt.Mod_cmb(B+i-2,i-1,N) * nt.Mod_cmb(H+W-i-B-1,H-i,N) % N;
            ans = ans % N;
        }
        Console.WriteLine(ans);
    }
}