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())
da = []
db = []
dc = []
for i in range(1,a+1):
    if a%i == 0:
    	da.append(i)

for j in range(1, b+1):
    if b%j == 0:
    	db.append(j)

for l in da:
    if l in db:
    	dc.append(l)

dc.sort(reverse = True)
print(dc[k-1])