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: Time Limit Exceeded)

def moddividedbyprime x, p
    power = x
    result = 1
    pminus2 = p - 2
    for i in 0...(pminus2.to_s(2).size)
        result = (result * power) % p if pminus2[i] == 1
        power = (power ** 2) % p
    end
    return result
end

def counting x, y
    count = 1
    sum = x + y
    [x, y].min.times{|i|
        count *= (sum - i) % 1_000_000_007
        count *= moddividedbyprime(i + 1, 1_000_000_007)
        count %= 1_000_000_007
    }
    return count
end

h, w, a, b  = gets.chomp.split.map{|s| s.to_i - 1}

right = b
right2 = w - b - 1
count = 0
for i in (0..(h - a - 1))
    count += (counting(right, i) * counting(right2, h - i)) % 1_000_000_007
    count %= 1_000_000_007
end
puts count