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>
#include <stdlib.h>
#include <string.h>

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

	int ans, count;
	if (a >= b) {
		ans = b;
	} else {
		ans = a;
	}
	for (count = 0; ; ans--) {
		if (a % ans == 0 && b % ans == 0) {
			count++;
		}
		if (count == k) {
			break;
		}
	}
	printf("%d\n", ans);
	return 0;
}