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.util.*;

/* 
 * 取模运算中的除法计算
 * （m + n） ! / (m! * n !)
 * 因为阶乘都被取模操作过， 所以除法时会出现问题
 * 本算法完美解决了此问题
 * */
public class Main {
	
	static int H, W, A, B;
	
	static final int MOD = 1000000007;
	
	public static void main(String[] args) {
		
		Scanner cin = new Scanner(System.in);
		
		/*input*/
		
		H = cin.nextInt();
		W = cin.nextInt();
		A = cin.nextInt();
		B = cin.nextInt();
		
		
		/* start */
		
		//get 
		long[] f = new long[W + H + 1];
		f[0] = 1;
		for (int i = 1; i < f.length; i ++) {
			f[i] = i * f[i-1];
			f[i] %= MOD;
		}
		
		
		//step1
		
		long res = 0;
		
		for (int j = B; j < W; j ++) {
			res += (comb((H - A - 1) + j, j, f) * 
				   comb((A - 1) + (W - j - 1), A - 1, f)) % MOD;
			res %= MOD;
		}
		
		res += MOD;
		res %= MOD;
		
		
		
		/*finish*/	
		System.out.println(res);
		
	}
	
	
	public static long mod_inv(long a, long m){
		return (a == 1 ? 1 : (1 - m*mod_inv(m%a, a)) / a + m);
	}
	
	public static long comb(int n, int k, long[] fact){
		if(n == 0){ return 1; }
		if(k == 0){ return 1; }
		
		return (((fact[n] * mod_inv(fact[k], MOD)) % MOD) * mod_inv(fact[n - k], MOD)) % MOD;
	}
}