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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

# frozen_string_literal: true

h, w, a, b = gets.split.map(&:to_i)

@f = {0=>1,1=>1}

def factorial(n)
  if @f.keys.last < n
    @f.keys.last.upto(n) { |i| @f[i] ||= @f[i - 1] * i }
  end
  @f[n]
end

def permutation(n, r)
  factorial(n) / factorial(n - r)
end

def combination(n, r)
  permutation(n, r) / factorial(r)
end

y1 = h - a - 1
pattern = (b..(w - 1)).inject(0) do |s, x1|
  y2 = h - 1 - y1 - 1
  x2 = w - 1 - x1
  s + combination(y1 + x1, x1) * combination(y2 + x2, x2)
end
p(pattern % (10**9 + 7))