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: Wrong Answer)

#include <stdio.h>
int main()
{
	int a, b, k;

	scanf("%d", &a);
	scanf("%d", &b);
	scanf("%d", &k);

	int i, count = 0, answer;

	for(i = 1;i < 101; i++)
	{
		if(a % i == 0 && b % i == 0)
		{
			count++;
		}
		if(count == k)
		{
			answer = i;
			break;
		}
	}

	printf("%d\n", answer);

	return 0;
}