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 (7.3.0) (judge verdict: Runtime Error)

def euclidean(a,b):
  _ = a % b
  while 1:
    if b % _ == 0:
      break
    else:
      _ = b % _
    return _

A, B, K = map(int, input().split())

a = max(A, B)
b = min(A, B)
e = euclidean(a, b)

by = []
r = int(e ** (1 / 2))

for i in range(1, r + 1):
  if e % i == 0:
    by.append(i)
    j = e // i
    if j != i:
      by.append(j)
by.sort()
print(by[K - 1])