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: Wrong Answer)

inputs = STDIN.readlines.map{|line|line.strip.split()}
line = inputs.shift

a = line[0].to_i
b = line[1].to_i
k = line[2].to_i
i = 0
Range.new(1, 100).each do |n|
    if a % n == 0 && b % n == 0 then
        i += 1
        if i == k then
            puts(n)
            break
        end
    end
end