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 = [int(_) for _ in input().split()]
mod = 10**9 + 7
 
X = [i for i in range(H + W + 1)]
X[0] = 1
for i in range(2, H + W + 1):
    X[i] = X[i - 1] * i % mod
 
Y = X.copy()
Y[-1] = pow(Y[-1], mod - 2, mod)
for i in range(H + W, 1, -1):
    Y[i - 1] = i * Y[i] % mod
 
 
def comb(x, y):
    return X[x] * Y[y] * Y[x - y] % mod
 
 
ans = 0
for i in range(B, min(B + H - A, W)):
    ans += comb(H - A + B - 1, i) * comb(W + A - B - 1, W - i - 1)
    ans %= mod
print(ans)