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(" "))
div = 10 ** 9 + 7
size = h + w - 1

fact = [0] * size
inverse = [0] * size
inv_calced = [0] * size
fact[:2] = [1, 1]
inverse[:2] = [1, 1]
inv_calced[:2] = [0, 1]

for i in range(2, size):
  fact[i] = fact[i - 1] * i % div
  inv_calced[i] = -inv_calced[div % i] * (div // i) % div
  inverse[i] = inverse[i - 1] * inv_calced[i] % div
  
result = 0
for x in range(b, w):
  y = h - a - 1
  temp_1 = (fact[x+y] * inverse[x] % div) * inverse[y] % div
  temp_2 = (fact[h+w-x-y-3] * inverse[w-x-1] % div) * inverse[h-y-2] % div
  result += ((temp_1 % div) * (temp_2 % div)) % div

print(result % div)