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)

amari = 10**9 + 7

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

matrix = Array.new(w, [])
w.times do |i|
  matrix[i] = Array.new(h, 0)
end

w.times do |i|
  h.times do |j|
    matrix[i][j] = if i + 1 <= b && (h - a) <= j
                     puts "i=#{i}, j=#{j}"
                     0
                   elsif i == 0 || j == 0
                     1
                   else
                     matrix[i - 1][j] + matrix[i][j - 1]
                   end
  end
end

puts matrix.last.last % amari