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 Python (3.4.3) (judge verdict: Runtime Error)

import math

a, b, k = map(int, input().split())
gcd = math.gcd(a, b)
divisor_list = []

if gcd == 1:
    divisor_list = [1]
else:
    divisor_list.append(1)
    for i in range(2, gcd // 2 + 1):
        if gcd % i == 0:
            divisor_list.append(i)
    divisor_list.append(gcd)

print(divisor_list[len(divisor_list)-1-k+1])