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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>

using namespace std;



int factrial(int n){
	if(n<=1){
		return 1;
	}else{
		return n*factrial(n-1);
	}
}
int combination(int a,int b){
	return factrial(a+b)/(factrial(a)*factrial(b));
}

int func(int H,int W,int i,int j){
	int tmp1,tmp2;
	tmp1=combination(i-1,j-1);
	tmp2=combination(W-i,H-j);
	return tmp1*tmp2;
}

int main(){
	int H,W,A,B;
	int x,y;
	int count=0;
	int a=1000000000+7;


	cin>>H>>W>>A>>B;

	y=H-A+1-1;
	x=B+1;
	while( (y>0) && (x<=W)){
		count=count+func(H,W,x,y);
		count=count%a;

		x=x+1;
		y=y-1;
	}
	cout<<count<<endl;

	return 0;
}