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)

a, b, k = map(int, input().split())

def euclidean(a,b):
    if a < b:
        tmp = a
        a = b
        b = tmp
    if a%b != 0:
        return euclidean(a%b, b)
    else:
        return b

n = euclidean(a, b)
for i in range(n , 0, -1):
  if a % i == 0 and b % i == 0:
    k -= 1
    if k ==0:
      print(i)
      exit()