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: Accepted)

require 'prime'

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

primes = Prime.prime_division(a.gcd(b)).map do |n, p|
  [n]*p
end.flatten


divisors = (1..primes.size).to_a.map do |n|
  primes.combination(n).map do |arr|
    arr.inject(:*)
  end
end.flatten + [1]

puts divisors.uniq.sort.reverse.at(k-1)