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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun calc-gcd (a b)
  (if (zerop (mod a b)) b (calc-gcd b (mod a b))))

(defun calc-divisor (a)
  (loop :for x :from 1 :to a
        :when (zerop (mod a x))
        :collect x))

(defun solve (a b k)
  (let* ((gcd (calc-gcd a b))
         (divisors (calc-divisor gcd)))
    (nth (1- k) (reverse divisors))))


(defun main ()
  (let* ((a (read))
         (b (read))
         (k (read)))
    (format t "~A~%" (solve a b k))))

(main)