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)

n = gets.split
a = n[0].to_i
b = n[1].to_i
k = n[2].to_i

numbers = [a,b]
max = numbers.max {|a, b| a.to_i <=> b.to_i }
result = []

(1..max).each do |i|
  if((a/i) * i == a)
    if((b/i) * i == b)
      result.push(i)
    end
  end
end

p result[k-1]