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)

from fractions import Fraction

data = input().split()
a = int(data[0])
b = int(data[1])
k = int(data[2])

def fuc(left, right):
    val = Fraction(left, right)
    ans = val.denominator
    while ans%2 ==0:
        ans=ans//2
    while ans%5 ==0:
        ans=ans//5
    return ans==1

ans = []
i=0
while True:
    i+=1
    if fuc(a, i) and fuc(b, i) == 0:
        ans.append(i)
    if len(ans) > k:
        break

print(ans[k-1])