Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in Julia (0.5.0) (judge verdict: Accepted)

function mkdivisor(n::Int) 
  divisors=Int[] 
  for i=1:div(n^0.5,1) 
    if n%i==0 
      push!(divisors,i) 
      if i!= fld(n,i); push!(divisors,fld(n,i));end
    end
  end
  sort!(divisors)
  return divisors
end

macro p(z);:((x->parse(Int,x)).(split($z)));end
a,b,k=@p(readline())
print([i for i=mkdivisor(a) if i in mkdivisor(b)][end-k+1])