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: Time Limit Exceeded)

from math import *

p = 1000000007
ft = []
ift = []

def make_ft(max):
    x = 1
    ft.append(x)
    # ft[i] == i!
    for i in range(1, max+1):
        x *= i
        x %= p
        ft.append(x)
    return

# i!^-1 == i!^(p+2) (mod p)
def make_ift(max):
    ift.append(1)
    for i in range(1, max+1):
        invf = 1
        x = ft[i]
        for j in range(ceil(log2(p-2))):
            # x == i!^2^j
            if ((p - 2) >> j) & 1:
                invf *= x
                invf %= p
            x *= x
            x %= p
        ift.append(invf)
    return

def combination(a, b):
    res = ft[a] * ift[b] * ift[a-b]
    res %= p
    return res

def main():
    H, W, A, B = list(map(int, input().split()))

    make_ft(H+W)
    make_ift(H+W)
    ans = 0
    for i in range(H-A):
        ans += combination(B+i-1, i) * combination(W-B+H-i-2, H-i-1)
        ans %= p

    print(ans)

if __name__ == '__main__':
    main()