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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

A, B, K = map(int, input().split())
N = min(A, B)
list_gcd = [] 

for i in range(1, N):
  if A % i == 0 and B % i == 0:
    list_gcd.append(i)
    
if N == 1:
  Y = max(A,B)
  if Y == 1:
    list_gcd.append(1)
  else:
    for i in range(1, Y):
      if Y % i == 0:
        list_gcd.append(i)
    
print(list_gcd[K-1])