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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h> 
#include<stdlib.h>



int main ()  {
	int i,nb,a,b,k ;
	
	scanf("%d %d %d",&a,&b,&k) ;
	nb=1 ;
	i=1 ;
	while (nb<k ) {
	i++ ;
	if (a%i==0 && b%i==0)	{
		nb++ ;
		}
		

	}
	printf("%d",i) ;
	
	return(0) ;
}