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)

args = gets.split(" ").map(&:to_i)

input_a = args[0]
input_b = args[1]
input_K = args[2]

calc_divisor = lambda{|input| (1..input).select do |i|
                                 input.modulo(i) == 0
                              end}
if (input_a <= input_b)
  divisors_list = calc_divisor.call(input_a)
  res = divisors_list.select{|div| input_b.modulo(div) == 0}.sort.reverse
else
  divisors_list = calc_divisor.call(input_b)
  res = divisors_list.select{|div| input_a.modulo(div) == 0}.sort.reverse
end

puts res.at(input_K - 1)