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)

h, w, a, b = map(int, input().split())
###############
# 二項係数テンプレート
# 出力制限
mod = 10 ** 9 + 7
MAX_N = 2 * 10 ** 5
factorial = [1] * MAX_N
#事前に階乗テーブルを用意
def calc_factorial():
    for i in range(1, MAX_N):
        factorial[i] = i * factorial[i - 1] % mod

def comb(n, k):
    a = factorial[n] % mod
    b = (factorial[k] * factorial[n - k]) % mod
    b_ = pow(b, mod - 2, mod)
    return (a * b_) % mod


# 階乗を用意
calc_factorial()
#########

# 全体の組み合わせを計算する
# h-1(高さ)+w-1(横幅)から、h-1(高さ)個取り出す組み合わせ
all = comb(h + w - 2, h - 1)
sub = 0
for j in range(1, b + 1):
    sub += comb(h - a - 1 + j - 1, j - 1) * comb(a - 1 + w - j, w - j)
    sub = sub % mod
if all - sub <= 0:
    print(all - sub + mod)
else:
    print(all - sub)