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: Accepted)

a, b, k = gets.split().map{|n| n.to_i}

a_list = []
a.times do |n|
    n += 1

    if a % n == 0
        a_list.push(n)
    end
end

b_list = []
b.times do |n|
    n += 1

    if b % n == 0
        b_list.push(n)
    end
end

ans_list = a_list & b_list

puts ans_list[-k]