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 (Clang 3.8.0) (judge verdict: Accepted)

#include<stdio.h>
main()
{
	int a,b,c,flag,d = 1;
	int num[200],i,j,k;
	scanf("%d %d %d",&a,&b,&c);
	if(a > b)
	flag = b;
	else flag = a;
	for(i = flag; i > 0; i--)
	{
		if(a % i == 0&&b % i == 0)
		{
		 num[d] = i; 
		 d++;
	    }
	}
   printf("%d",num[c]);
}