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)

def gcd(a,b):
    x=max(a,b)
    y=min(a,b)
    if x%y==0:
        return y
    else:
        return gcd(y,x%y)
A,B,K=map(int,input().split())
G=gcd(A,B)
L=[]
for i in range(1,G+1):
    if G%i==0:
        L.append(i)
L.sort(reverse=True)
print(L[K-1])