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 Ruby (2.3.3) (judge verdict: Runtime Error)

A, B, C = gets.chomp.split.map(&:to_i)
#B = gets.chomp.split.map(&:to_i)
res = 0
k = 0
if A > B 
    N=B
else 
    N=A
end

while 0 < N
    if A % (N) == 0 && B % (N) == 0 then
        k += 1
        if C== k then
            puts N
            exit!
        end
    N -= 1
end