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)

ar = gets.chomp.split(" ").map{|i|i = i.to_i}
a=ar[0]
b=ar[1]
k=ar[2]
def gcd(a,b)
    while b>0 do
        a,b = b,a%b
    end
    return a
end
ar = []
gcd=gcd(a,b)
gcd.times do|i|
    if gcd % (i+1)==0 then
        ar<<(i+1)
    end  
end
ar.uniq!
ar.sort!
pp ar[ar.length-k]