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)

def gcd(a, b)
  a, b = b, a if a < b
  r = a % b
  r == 0 ? b : gcd(b, r)
end
a, b, k = gets.chomp.split(' ').map(&:to_i)
ab = gcd(a, b)

counter = 0
100.downto(1) do |i|
  counter += 1 if ab % i == 0
  if counter == k
    puts i
    break
  end
end