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>

int main()
{
	int A,B,K,num;
	scanf("%d %d %d",&A,&B,&K);
	if ( A > B ){
		num = B;
	} else {
		num = A;
	}

	while(1) {
		if ( ( A % num == 0 ) && ( B % num == 0 ) ) {
			K--;
		}
		if ( K == 0 ) break;
		num--;
	}

	printf("%d\n",num);
	return 0;
}