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 (2.7.1) (judge verdict: Accepted)

#!/usr/bin/env ruby
a, b, k = gets.chomp.split.map(&:to_i)

yakusu = []
common_yakusu = []

if a > b
  1.upto(b) do |i|
    yakusu << i if b % i == 0
  end

  yakusu.each do |y_i|
    common_yakusu << y_i if a % y_i == 0
  end

  common_yakusu = common_yakusu.reverse

  puts common_yakusu[k - 1]
else
  1.upto(a) do |i|
    yakusu << i if a % i == 0
  end

  yakusu.each do |y_i|
    common_yakusu << y_i if b % y_i == 0
  end

  common_yakusu = common_yakusu.reverse

  puts common_yakusu[k - 1]
end