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)

#!/bin/ruby

a, b, k = gets.chomp.split(" ").map(&:to_i)

divide = 1
cnt = 0
dividable_numbers = []
while true
  if a % divide == 0 && b % divide == 0
    dividable_numbers << divide
    cnt += 1
    divide += 1
  else
    divide += 1
  end
  break if divide > a || divide > b
end
puts dividable_numbers[-k]