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: Accepted)

#include<bits/stdc++.h>
#define Mod 1000000007
#define Val(x) (((long long)x) % Mod)
#define maxn 200005
using namespace std;
int fac[maxn];
int Pow(int a,int n) {
	int ret = 1;
	int base = a;
	while(n) {
		if(n&1)	ret = Val(ret*base);
		base = Val(base*base);
		n >>= 1;
	}
	return ret;
}
int cal(int n,int m) {
	return Val(Val(fac[n+m]*Pow(fac[n],Mod-2))*Pow(fac[m],Mod-2));
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	fac[0] = 1;
	for(int i=1;i<maxn;i++)
		fac[i] = Val(fac[i-1] * i);
		
	int n,m,a,b;
	cin >> n >> m >> a >> b;
	
	int ans = 0;
	for(int j=b+1;j<=m;j++)
		ans = Val(ans + Val(cal(n-a-1,j-1)*cal(a-1,m-j)));
	
	cout << ans << endl;
	return 0;
}