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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
    implicit none

    integer A,B,K,i,count
    count = 0

    read(*,*) A,B,K

    do i = max(A,B),1
        if (mod(A,i)==0 .and. mod(B,i)==0)then
            count = count + 1
            if (count == K) then
                write(*,"(I0)") i
                exit 
            end if
        end if
    enddo

end program main