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.

Examples

Input

8 12 2

Output

2

Input

100 50 4

Output

5

Input

1 1 1

Output

1

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