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 Python (3.4.3) (judge verdict: Accepted)

def solve():
	h,w,a,b = map(int, input().split())
	mx = max(h,w)
	mod = 10**9+7
	fac = [1]*(h+w+1)
	for i in range(1,h+w+1):
		fac[i] = fac[i-1]*i%mod
	inv = [1]*(mx+1)
	inv[-1] = pow(fac[mx], mod-2, mod)
	for i in range(mx-1, -1, -1):
		inv[i] = inv[i+1]*(i+1)%mod
	const = inv[h-a-1]*inv[a-1]%mod
	ans = sum(fac[h-a+i-1]*inv[i]*fac[a+w-2-i]*inv[w-i-1]%mod for i in range(b,w))
	print(ans*const%mod)

if __name__=="__main__":solve()