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 $B$.