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)

h, w, a, b = gets.chomp.split.map(&:to_i)
$M = 10**9+7

r = [1]
for i in 1..200000 do
    r[i] = r[i-1] * i % $M
end

##p r.size
def my_pow(x,n)
    ans = 1
    while n > 0
        if n % 2 == 1
            ans = ans * x % $M
        end
        x = x * x % $M
        n /= 2
    end
    return ans
end


rr = [1]
for i in 1..200000 do
    rr[i] = my_pow(r[i], $M - 2)
#    puts rr[i]
end

def combi(n,k,r, rr)
    k=n-k if 2*k > n
    return 1 if k == 0
    return r[n] * rr[n-k] * rr[k]
end

ans = 0
(1).upto(h-a) do |i|
    aaa = combi(i+b-2, b-1, r, rr)
    bbb = combi(h-i+1+w-b-2, w-b-1, r, rr)
    ans += aaa * bbb % $M
end
puts ans % $M