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 <time.h>

int main(){
	int a,b,c,d;
	int x[256],y[256];
	int p=1;
	int cc;
	
	scanf("%d %d %d",&a,&b,&d);
	
	c=a;
	if(a>b){
	c=b;
	}
	
	x[0]=1;
	for(int i=2;i<=c;i++){
		if(a%i==0&&b%i==0){
			x[p]=i;
			p++;
		}
	}
	cc=p;
	p--;
	
	for(int i=0;i<cc;i++){
		y[i]=x[p];
		p--;
	}
	
	printf("%d",y[d-1]);
	
	return 0;
}