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: Runtime Error)

um_a,num_b,num_k = gets.split(" ").map!{|i| i.to_i}
list_com = Array.new

count = 1 
while count <= num_a + num_b 
  if num_a%count == 0 && num_b%count == 0
    list_com.push(count)
  end
  count += 1
end

list_com.reverse!
#p list_com
p list_com[num_k-1]