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 getlist():
	return list(map(int, input().split()))
H, W, A, B = getlist()
H -= 1
W -= 1
N = H + W + 2

const = 10 ** 9 + 7
fac = [0] * (N + 1)
inv = [0] * (N + 1)
finv = [0] * (N + 1)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, N + 1):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

ans = 0
i = 0
while H - A - i > 0 and W - B - i > 0:
	ans += fac[H - A + B] * finv[B + i] * finv[H - A - i] * fac[W - B + A] * finv[A + i] * finv[W - B - i]
	ans %= const
	i += 1

if H - A - i == 0:
	ans += fac[W - B + A] * finv[A + i] * finv[W - B - i]
else:
	ans += fac[H - A + B] * finv[B + i] * finv[H - A - i]

ans %= const
print(ans)