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: Accepted)

# -*- coding: utf-8 -*-


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

# print(A, K)

set_A = set()
set_B = set()

for i in range(1, A + 1):
    if A % i == 0:
        set_A.add(i)


for i in range(1, B + 1):
    if B % i == 0:
        set_B.add(i)

# print(set_A ,set_B)

seki = set_A & set_B

seki = list(seki)

seki.sort(reverse=True)

print(seki[K - 1])