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())
mx = max(a, b) * 0.5
match, ans = 0, 0

for i in range(mx):
    if ((a % (mx - i)) == 0) 
    and ((b % (mx - i)) == 0):
        match += 1
        ans = mx - i
        
        if match == k:
            break
print(ans)