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)

line = gets.chomp.split.map(&:to_i)
a = line[0]
b = line[1]
k = line[2]

times = 0
ans = 0
i = a < b ? b : a
while i > 0 do
    if a % i == 0 and b % i == 0
        times += 1
        ans = i
    end
    break if times == k
    i -= 1
end

puts ans