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>

int main(void)
{
	int a, b, k;
	int l;
	int lx[100];
	
	int i, j;
	
	scanf("%d%d%d", &a, &b, &k);
	
	if (a <= b) {
		l = a;
	}
	else {
		l = b;
	}
	
	for (i = 1, j = 1; i <= l; i++){
	
		if (a % i == 0 && b % i == 0){
			lx[j] = i;
			j ++;
		}
	}
	
	printf("%d", lx[k]);
	
	
	return (0); 
}