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)

a,b,k = gets.split.map(&:to_i)

require 'prime'

def divisor(n)
  return [1] if n == 1
  Prime.prime_division(n).map do |e|
    Array.new(e[1]+1).map.with_index do |element, i|
      e[0]**i
    end
  end.inject{|p,q| p.product(q)}.map do |a|
    [a].flatten.inject(&:*)
  end.sort
end
a_a = divisor(a)
b_b = divisor(b)
ans = a_a & b_b
puts ans[k-1]