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: Accepted)

#include <stdio.h>

int main() {
	int i, j, a, b, k;
	int x[100], xsoe = 0;

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

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

	printf("%d\n", x[xsoe - k]);

	return 0;
}