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: Runtime Error)

require 'prime'
a,b,c=gets.split.map &:to_i
class Integer
  def my_divisor_list
    divisors,primes=[1],[]
    Prime.prime_division(self).each do |prime|
      prime[1].times {primes << prime[0]}
    end
    1.upto(primes.size) do |i|;primes.combination(i) do |prime|
      divisors << prime.inject{|a,b| a *= b}
    end;end
    divisors.uniq!.sort!
    return divisors
  rescue ZeroDivisionError
    return
  end
end
p (a.my_divisor_list&b.my_divisor_list).reverse[c-1]