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 Ruby (2.3.3) (judge verdict: Wrong Answer)

require 'bigdecimal'
require 'bigdecimal/util'
def ore a,b
  n = a.to_d.quo b.to_d
  a.to_d == n*b.to_d
end

a,b,k = gets.chomp.split().map(&:to_i)
max=[a,b].max
(1..max).each do |n|
  if ore(a,n) && ore(b,n)
     k-=1
    if k==0
      puts n
      break
    end
  end
end