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: Runtime Error)

import java.util.ArrayList;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	static int size;
	
	static boolean isTop(ArrayList<Integer> nArr, int i){
		if(i == nArr.size()-1) return true;
		else return false;
	}
	
	static void addArr(ArrayList<Integer> nArr, int i){
		nArr.set(i, 0);
		if(nArr.get(i+1) == 9){
			addArr(nArr, i+1);
		}else{
			nArr.set(i+1, nArr.get(i)+1);
		}
	}
	public static void main(String[] args) {
		Scanner scan = new  Scanner(System.in);
		StringTokenizer strToken = new StringTokenizer(scan.nextLine(), " ");
		StringTokenizer digitToken = new StringTokenizer(scan.nextLine(), " ");
		ArrayList<Integer> disLikes = new ArrayList<Integer>();
		
		StringBuffer N = new StringBuffer(strToken.nextToken());
		StringBuffer K = new StringBuffer(strToken.nextToken());
		
		while(digitToken.hasMoreTokens()){
			disLikes.add(Integer.parseInt(digitToken.nextToken()));
		}
		
		//돈을 자리수 대로 stack에 쌓는다
		ArrayList<Integer> nArr = new ArrayList<Integer>();
		N = N.reverse();
		for(int i=0; i<N.length(); i++){
			nArr.add(Integer.parseInt(Character.toString(N.toString().charAt(i))));			
		}
		
		size = nArr.size();
		
		for(int i=0; i<size; i++){
			while(true){
				if( disLikes.contains(nArr.get(i)) ){
					if(nArr.get(i) == 9){
						if(isTop(nArr, i)){
							nArr.add(1);
							nArr.set(i, 0);
							size++;
						}else{
							addArr(nArr, i);
						}
					}else{
						nArr.set(i, nArr.get(i)+1);
					}
				}else{
					break;
				}	
			}
		}
		
		String print="";
		
		for(int i=nArr.size()-1; i >=0; i-- ){
			print += nArr.get(i);
		}
		
		System.out.println(print);
	}
}