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.strip.split.map(&:to_i)
MOD = 10**9+7

def power(x, n)
  return 1 if n.zero?

  if n.even?
    return power(x*x, n/2) % MOD
  else
    return x*power(x, n/2)**2 % MOD
  end
end

$fac = []
$fac[0] = $fac[1] = 1
2.upto(h+w) do |num|
  $fac[num] = num * $fac[num-1]
end

$ifac = []
$ifac[0] = $ifac[1] = 1
$ifac[h+w-2] = power($fac[h+w-2], (MOD-2)) % MOD
(h+w-3).downto(2) do |num|
  $ifac[num] = $ifac[num+1] * (num+1) % MOD
end

def comb(n,k)
  return 0 if n<k || n<0 || k<0
  $fac[n] * $ifac[n-k] * $ifac[k] % MOD
end

sum = 0
(b+1).upto(w) do |num|
  c1 = comb(h-a-1+num, num)
  c2 = comb(a-1+w-num+1, a-1)

  sum += c1*c2 % MOD
end

p sum

#p $fac
#p $ifac