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, j, k, f = 0, n, s, t;
	int mp = 0, a, b, c, d, e, x, y, z;
	int g[50];
	d = 1;

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

	for (i = 1;i<a;i++) {
		if (a%i == 0&& b%i == 0) {
				g[d] = i;
				d++;
		}

	}




	printf("%d", g[k]);
	return 0;
}