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())

max = max(A, B)
min = min(A, B)
max_k = 1
n = 0
L = []
for i in range(min,1,-1):
    # print(i)
    # if(n < K):
    if(min % i == 0 and max % i == 0):
        max_k = i
        n += 1
        L.append(max_k)

# print(max_k)
# print(L)
print(L[K-1])