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 minnum(int a,int b){
	if(a > b)return b;
	else return a;
}

int main(void){
	int a,b,k;
	int res;
	int c=1;
	scanf("%d %d %d",&a ,&b ,&k);
	int min = minnum(a,b);
	for(int i=1;i<min;i++){
		if(a % i == 0 && b % i == 0){
			res = i;
			if(c == k){
				printf("%d\n",res);
				break;
			}
			c++;
		}
	}
	return 0;
}