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: Runtime Error)

H, W, A, B = gets.split.map(&:to_i)
MOD = 1_000_000_007

def extended_gcd(a, b)
  r0, r = a.abs, b.abs
  x, x0, y, y0 = 0, 1, 1, 0
  while r != 0
    r0, (q, r) = r, r0.divmod(r)
    x, x0 = x0 - q*x, x
    y, y0 = y0 - q*y, y
    end
  [r0, x0 * (a < 0 ? -1 : 1)]
end

def mod_inv(n)
  g, x = extended_gcd(n, MOD)
  x % MOD
end

M = H + W
(2 .. M).each{|n| @f[n] = @f[n - 1] * n % MOD}
@fi = []; @fi[M] = mod_inv(@f[M])
M.downto(1){|n| @fi[n - 1] = @fi[n] * n % MOD}

def mod_c(a, b)
  @f[a] * @fi[a - b] * @fi[b] % MOD
end

def sq(h, w)
  return 1 if h * w == 0
  mod_c(h + w, h)
end

ans = (1 .. [H - A, W - B].min).inject(0) do |s, n|
  (s + sq(H - (A + n), B + n - 1) * sq(A + n - 1, W - (B + n))) % MOD
end
puts ans