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 (2.7.1) (judge verdict: Runtime Error)

class Integer
  def fac
    return 1 if self.zero?
    ary = (1..self).to_a
    loop do
      ary = ary.each_slice(2).map do |a, b|
        b ? a * b : a
      end
      return ary[0] if ary.size == 1
    end
  end

  def combi r
    self.fac / (r.fac * (self - r).fac)
  end
end



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

points = [(b + h - a - 1).combi(b) % (10 ** 9 + 7)]
((b + 1)..(w - 1)).each do |i|
  p i
  points.push (points[-1] * (i + h - a - 1)/i) % (10 ** 9 + 7)
end; 0

points.size

s = (w - b - 1 + a - 1).combi(w - b - 1) % (10 ** 9 + 7)
ans = points.each_with_index.reduce(0) do |sum, (point, idx)|
  sum = (sum + point * s) % (10 ** 9 + 7)
  s = s * (w - b - 1 - idx)/(w - b - 1 + a - 1 - idx)
  sum
end
puts ans