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.split.map(&:to_i)
k = 10 ** 9 + 7

fac = [1]
1.upto(h+w-2) do |i|
    fac << fac[i-1] * i % k
end
#p fac

s = "111011100110101100101000000101".reverse
rfac = Array.new(h+w-1,1)
t = fac[h+w-2]
s.each_char do |c|
    rfac[h+w-2] = (rfac[h+w-2] * t) % k if (c == '1')
    t = t ** 2 % k
end

(h+w-3).downto(0) do |i|
    rfac[i] = rfac[i+1] * (i+1) % k
end
#p rfac

ans = 0
1.upto(h-a) do |i|
    x = fac[b+i-2] * rfac[b-1] % k * rfac[i-1] % k
    y = fac[w-b+h-i-1] * rfac[w-b-1] % k * rfac[h-i] % k
    ans = (ans + x * y) % k
end

puts ans