K-th Common Divisor

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

inputFormat

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

outputFormat

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

样例

1 1 1

1