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 <math.h>
#include <string.h>
#define pai 3.1415926535

int main(void) {
	int A, B, K;
	scanf("%d%d%d", &A, &B, &K);
	int count = 0;
	int a;
	for (int i = 1; i <= A; i++) {
		if ((A%i == 0) && (B%i == 0)) {
			count++;
			if (count == K) {
				a = i;
				break;
			}
		}
	}


	printf("%d", a);
	return 0;
}