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

#define GYOU_MAX 256

int main(void) {

	int A, B, K;
	scanf("%d%d%d", &A, &B, &K);

	int count = 0;
	int X[100];
	for (int i = 1;i<=100; i++) {
		if (A%i == 0 && B%i == 0) {
			X[count] = i;
			count++;
		}
	}

	printf("%d\n", X[count - K]);

	return 0;
}