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 ext_euclid(a, b):
    # return (x, y, gcd(a, b)) such that a * x + b * y = gcd(a, b)
    if b == 0:
        return 1, 0, a
    y, x, v = ext_euclid(b, a % b)
    y -= (a // b) * x
    return x, y, v


def mod_inv(a, mod):
    x, _, _ = ext_euclid(a, mod)
    return x % mod


def comb_list_1(H, W, A, B, mod, modinv_list):
    # (h+B-1)_C_(B-1)  (h in {0, ..., H-A-1})
    ret = [0 for _ in range(H - A)]
    c = 1
    for h in range(H - A):
        ret[h] = c
        c *= h + B
        c *= modinv_list[h + 1]
        c %= mod
    return ret


def comb_list_2(H, W, A, B, mod, modinv_list):
    # (-h+H+W-B-2)_C_(W-B-1)  (h in {0, ..., H-A-1})
    ret = [0 for _ in range(H - A)]
    # initial value -> (A+W-B-1)_C_(W-B-1)  (h = H-A-1)
    c = 1
    for a in range(1, A + 1):
        c *= (a + W - B - 1)
        c *= modinv_list[a]
        c %= mod
    # fill elements of result list from the back
    for h in range(H - A - 1, -1, -1):
        ret[h] = c
        c *= H - h + W - B - 1
        c *= modinv_list[H - h]
        c %= mod
    return ret


def main():
    MOD = 10 ** 9 + 7
    H, W, A, B = list(map(int, input().split(' ')))
    modinv_list = [None] + [mod_inv(h, MOD) for h in range(1, H + 1)]  # modinv doesn't exist on h = 0
    combs_1 = comb_list_1(H, W, A, B, MOD, modinv_list)
    combs_2 = comb_list_2(H, W, A, B, MOD, modinv_list)
    ans = 0
    for c1, c2 in zip(combs_1, combs_2):
        ans += c1 * c2
        ans %= MOD
    print(ans)


if __name__ == '__main__':
    main()