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)

A,B,K = map(int,input().split())
x = [A, B]
x.sort()
res = [1]
res_n=[1]
i = 2

while i <= x[0]:
    if x[0] % i == 0 and x[1] % i == 0:
        x = [x[0] / i, x[1] / i]
        res.append(i)
    else:
        i += 1

print(res[K-1])