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: Wrong Answer)

H, W, A, B = gets.split(" ").map(&:to_i)

=begin
cache = Hash.new { |h, k| h[k] = Hash.new }

def routes(i, j, cache)
  puts "#{i}, #{j}"
  if i == 0 && j == 0
    return 1
  else
    c = 0
    c += cache[i - 1][j] || routes(i - 1, j, cache) if i - 1 >= 0 && j >= 0 && !(i > (H - A - 1) && j < B)
    c += cache[i][j - 1] || routes(i, j - 1, cache) if i >= 0 && j - 1 >= 0 && !(i > (H - A - 1) && j < B)
    cache[i][j] = c
    return c
  end
end

puts routes(H - 1, W - 1, cache)
=end

cache = Hash.new { |h, k| h[k] = Hash.new(0) }
cache[0][0] = 1

H.times do |i|
  (i > (H - A - 1) ? B.upto(W) : W.times).each do |j|
    next if i > (H - A - 1) && j < B
    cache[i][j] += cache[i - 0][j - 1] if i - 0 >= 0 && j - 1 >= 0
    cache[i][j] += cache[i - 1][j - 0] if i - 1 >= 0 && j - 0 >= 0
  end
end

puts cache[H - 1][W - 1]