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)

def create_fact_mod(num_max, mod)
    $fmod = Array.new(num_max + 1)
    $fmod[0] = 1
    $fmod[1] = 1
    (2..num_max).each do |i|
        $fmod[i] = ($fmod[i - 1] * i) % mod
    end
end

def create_seq_inv_mod(num_max, mod)
    $simod = Array.new(num_max + 1)
    $simod[0] = 1
    $simod[1] = 1
    (2..num_max).each do |i|
        $simod[i] = (mod - mod / i) * $simod[mod % i] % mod
    end
end

def create_fact_inv_mod(num_max, mod)
    $fimod = Array.new(num_max + 1)
    $fimod[0] = 1
    $fimod[1] = 1
    (2..num_max).each do |i|
        $fimod[i] = ($fimod[i - 1] * $simod[i]) % mod
    end
end

def create_mod_tables(n, mod)
    create_fact_mod(n, mod)
    create_seq_inv_mod(n, mod)
    create_fact_inv_mod(n, mod)
end

def comb_mod(n, k, mod)
    return $fmod[n] * $fimod[n - k] * $fimod[k] % mod
end


H, W, A, B = gets.split.map(&:to_i)
MOD = 10**9+7

create_mod_tables(H+W, MOD)

sum = 0
i = 1
loop do
    w = B + i
    h = A + i
    break if w > W || h > H
    c1 = comb_mod(H-h+w-1, w-1, MOD)
    c2 = comb_mod(h+W-w-1, h-1, MOD)
    sum += c1 * c2 % MOD
    sum %= MOD
    i += 1
end
puts sum