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: Wrong Answer)

import sys


def input():
    return sys.stdin.readline()[:-1]

# N = int(input())
# A = [int(x) for x in input().split()]
# a, b, c = map(int, input().split())
# name1 = str(input())
# alph = {"A": 1, "B": 2, "C": 3, "D": 4, "E": 5}
# b = list(map(lambda x: math.ceil(x/10)*10, a))


a, b, k = map(int, input().split())
ans = 0
for i in range(max(a, b)+1):
    if i == 0:
        continue
    if a % i == 0 and b % i == 0:
        ans += 1
    if ans == k:
        print(i)
        break