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 Lua (5.3.2) (judge verdict: Accepted)

a,b,k = io.read("n","n","n")
t = {}
for i=1,math.max(a,b) do
    q1 = a % i
    q2 = b % i
    if (q1 == 0 and q2 == 0) then
        table.insert(t, i)
    end
end
print(t[#t + 1 - k])