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 Julia (0.5.0) (judge verdict: Wrong Answer)

function main()
  
  (A,B,K) = map(x -> parse(Int,x), split(readline()))
  
  count = 0
  
  for i in 1:A*B

    if A % i == 0 && B % i == 0
      count += 1
    end

    if count == K
      println(i)
      break
    end
    
  end
  
end

main()