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 Lua (5.3.2) (judge verdict: Accepted)

A,B,K=io.read("n","n","n")
function d(a,b)
    if a%b==0 then
        return b
    end
    local c=a%b 
    return d(b,c)
end
local mod=d(A,B)
local count=0
for i=mod,1,-1 do
    if A%i==0 and B%i==0 then
        count=count+1
    end
    if count==K then
        print(i)
        break
    end
end