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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
public class Main
{
	
	private void solve()throws IOException
	{
		fact();
		int h=nextInt();
		int w=nextInt();
		int a=nextInt();
		int b=nextInt();
		long ans=0;
		for(int i=b+1;i<=w;i++)
			ans=(ans+(choose(h-a-1+i-1,h-a-1)*choose(w-i+a-1,a-1))%mod)%mod;
		out.println(ans);
	}
	long choose(int n,int r)
	{
		return (((fact[n]*modinv(fact[r]))%mod)*modinv(fact[n-r]))%mod;
	}
	final int maxn=(int)(2e5);
	long fact[];
	void fact(){
		fact=new long[maxn+1];
		fact[0]=1;
		for(int i=1;i<=maxn;i++)
			fact[i]=(fact[i-1]*i)%mod;
	}
	final long mod=(long)(1e9+7);
	long modinv(long x){
	    return modpow(x,mod-2);
	}
	long modpow(long a,long b){
	    long ret=1;
	    while(b!=0)
	    {
	        if(b%2==1)
	            ret=(ret*a)%mod;
	        a=(a*a)%mod;
	        b=b/2;
	    }
	    return ret;
	} 


	 
	///////////////////////////////////////////////////////////

	public void run()throws IOException
	{
		br=new BufferedReader(new InputStreamReader(System.in));
		st=null;
		out=new PrintWriter(System.out);

		solve();
		
		br.close();
		out.close();
	}
	public static void main(String args[])throws IOException{
		new Main().run();
	}
	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;
	String nextToken()throws IOException{
		while(st==null || !st.hasMoreTokens())
		st=new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	String nextLine()throws IOException{
		return br.readLine();
	}
	int nextInt()throws IOException{
		return Integer.parseInt(nextToken());
	}
	long nextLong()throws IOException{
		return Long.parseLong(nextToken());
	}
	double nextDouble()throws IOException{
		return Double.parseDouble(nextToken());
	}
}