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 (GNU Fortran 9.2.1) (judge verdict: Accepted)

program main
integer :: a,b,k,cnt=0
read(*,*)a,b,k

do i = 100,1,-1
if(mod(a,i)==0 .and. mod(b,i)==0) cnt = cnt + 1
if(cnt == k) exit
end do

write(*,*) i
end program main