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 (3.8.2) (judge verdict: Accepted)

import sys
A,B,K = map(int,input().split())
#euclid algorithm
if A < B: 
    A, B = B, A
while A%B != 0:
    A,B = B,A%B

count = 0
for I in range(B,0,-1):
    if B % I == 0:
        count += 1
    if count == K:
        print(I)
        break