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 PyPy2 (7.3.0) (judge verdict: Wrong Answer)

def f(a):
	r = []
	for d in range(1,int(a ** 0.5) + 1):
		r.append(d)	
		if d * d != a: r.append(a/d)
	return r if r else [1]
a,b,k = map(int, raw_input().split(' '))
r = []
for d in f(a):
	if d in f(b):r.append(d)
r.sort()
print r[-k]