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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
int main()
{
	int a,b,k;
	int i,x[100]={0},y=0,c=0;
	scanf("%d %d %d",&a,&b,&k);
	if(a>b) y=a;
	else y=b;
	for(i=1;i<=y;i++){
		if(a%i==0&&b%i==0){
			x[c]=i;
			c++;
		}
	}
	printf("%d\n",x[c-k]);
	return 0;
}