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)

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

answer=[]
(1..100).each do |n|
  if a%n ==0 && b%n ==0
    answer << n
  end
end

# answer => [1,2,4]
n = answer.reverse
# answer =>[4, 2, 1]
# indexは0スタートなので -1する
puts n[k -1]