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)

H,W,A,B = gets.split(' ').map!(&to_i)

H=H0-1
W=W0-1
A=1
B=1

def conbination(n,k)
    if n==0 or k==0
        return 1
    else
        bunbo = (1..[k,n-k].min).inject(1,:*)
        bunshi = (([k,n-k].max+1)..n).inject(1,:*)
        return bunshi/bunbo
    end
end

max_conb = conbination(H+W,W)
#p max_conb

startpoints = Array.new
endpoints = Array.new

for x in 0..B do
    startpoints.push([H-A+1,x])
end
for y in H-A+1..H do
    endpoints.push([y,B])
end
#p startpoints
#p endpoints

invalid_conb = 0

startpoints.each do |s|
    endpoints.each do |e|
        #print s,e
        #puts ''

        c1=conbination(s[0]-1+s[1],s[0]-1)
        c2=conbination(e[0]-s[0]+e[1]-s[1],e[0]-s[0])
        c3=conbination(H-e[0]+W-e[1],H-e[0])
        conb = c1*c2*c3
        #p [c1,c2,c3]
        #puts conb
        invalid_conb += conb
    end
end
#puts invalid_conb
puts max_conb-invalid_conb