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 find_gcd a, b
  while a != b
    if a > b
      a = a - b
    else
      b = b - a
    end
  end

  return a
end

def find_kth gcd, a, b, k
  num = 1
  ks = []
  1.upto(gcd) do |n|
    if a % n == 0 && b % n == 0
      ks << n
      num += 1
    end
  end

  ks[-k]
end

input = gets
matcher = input.match(/(\d+)\s*(\d+)\s*(\d+)/)
a, b, k = matcher[1].to_i, matcher[2].to_i, matcher[3].to_i

gcd = find_gcd a, b
num = find_kth gcd, a, b, k

puts num