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)

require "openssl"
include OpenSSL
HI, WI, A, B = gets.split.map(&:to_i)
H = HI - 1
W = WI - 1
M = BN.new(10 ** 9 + 7)

$memo_f = []
$memo_calc = {}

def f(n)
  return BN.new(1) if n <= 0
  $memo_f[n] ||= (1..n).inject(BN.new(1)) { |i,j| $memo_f[j] = BN.new(i).mod_mul(j, M) }
end

def calc(h, w)
  $memo_calc[[h, w]] ||=
    $memo_calc[[w, h]] =
      f(h + w).mod_mul(
        (f(h).mod_mul(f(w), M)).mod_inverse(M),
        M
      )
end
p(
  (0..(H-A)).map do |h|
    calc(h, B - 1).mod_mul(calc(H - h, W - B), M)
  end.inject do |i, j|
    i.mod_add(j, M)
  end.to_i
)