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 2.0.3) (judge verdict: Wrong Answer)

(let ((a (read))
    (b (read))
    (k (read))
    (ans 0))

    (if (< a b)
        (let ((tmp a))
            (setq a b)
            (setq b tmp)
        )
    )
    (loop for i from 1 to a do
        (if (and (zerop (rem a i)) (zerop (rem b i)))
            (progn
                (decf k)
                (if (= k 0)
                    (progn
                        (princ i)
                        (return)
                    )
                )
            )
        )
    )
)