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: Accepted)

H,W,A,B = $stdin.gets.chomp.split(" ").map(&:to_i)
M = 1000000007

def modpow(n,r)
  b = n
  a = 1
  while r > 0
    if r%2 == 1
      a = (a * b) % M
    end
    b = (b * b) % M
    r = r / 2
  end
  a
end

$factor = [1]
$refact = [1]
(1..(H+W)).each{ |k|
  $factor << (($factor[-1] * k)%M) 
  $refact << modpow($factor[-1], M-2)
}

#p $factor
#p $refact

def c(n,k)
  (($factor[n] * $refact[n-k]) % M) * $refact[k] % M
end

puts (0...[H-A,W-B].min).map{ |k|
  i,j = H-1-A-k,B+k
  #$stderr.puts "#{i}, #{j}"
  c(i+j, i) * c(H-i-1+W-j-1, H-i-1) % M
}.inject(:+) % M