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: Runtime Error)

h, w, a, b = [int(i) for i in input().split()]

p = 10 ** 9 + 7
s = 0

fact = [1]

for i in range(1, h+w-2):
    fact.append(fact[i-1] * i % p)

rfact = [(h+w-2) % p]

for i in range(h+w-1, 0, -1):
    rfact.append(rfact[-1] * i % p)

rfact.reverse()

def comb(n, r):
    return fact[n]//fact[n-r]//%pfact[r]%p

for i in range(w-b):
    s += comb(h+w-a-2-i, w-1-i) * comb(a-1+i, a-1)%p

print(s%p)