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: Wrong Answer)

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

import math

def f(n):
  a1 = math.factorial(B + n + H - A - 1) % (10**9 + 7)
  a2 = math.factorial(W - B - 1 - n + A - 1) % (10**9 + 7)
  b1 = math.factorial(B + n) % (10**9 + 7)
  b2 = math.factorial(H - A - 1) % (10**9 + 7)
  b3 = math.factorial(W - B - 1 - n) % (10**9 + 7)
  b4 = math.factorial(A - 1) % (10**9 + 7)
  return a1 * a2 / b1 / b2 / b3 / b4

def sigma(func, frm, to):
  result = 0
  for i in range(frm, to+1):
    result += func(i)
  return result

print(sigma(f, 0, W-B-1))