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 main():
    def cmb(n, r, mod):
        if (r < 0 or r > n):
            return 0
        r = min(r, n-r)
        return g1[n] * g2[r] * g2[n-r] % mod

    mod = 10**9+7  # 出力の制限
    N = 10**6
    g1 = [1, 1]  # 元テーブル
    g2 = [1, 1]  # 逆元テーブル
    inverse = [0, 1]  # 逆元テーブル計算用テーブル

    for i in range(2, N + 1):
        g1.append((g1[-1] * i) % mod)
        inverse.append((-inverse[mod % i] * (mod//i)) % mod)
        g2.append((g2[-1] * inverse[-1]) % mod)

    H, W, A, B = map(int, input().split())

    ans = cmb((H+W-2), min(H, W)-1, mod)

    tmp = 0
    for i in range(B):
        t = cmb(H-A-1+i, i, mod)
        t *= cmb(W-1-i + A - 1, A-1, mod)
        tmp += t
        tmp %= mod
    print((ans - tmp) % mod)


main()