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>
//abc120-A
/*
int main(void)
{
	int a, b, c,d;
	scanf("%d %d %d", &a, &b, &c);

	if (b >= a * c)
	{
		printf("%d", c);
	}

	else
	{
		d = b / a;
		printf("%d", d);
	}
	return 0;
}*/
//abc120-B
int main(void)
{
	int a, b, k, tmp;
	int ans = 0, i, j;

	scanf("%d %d %d", &a, &b, &k);

	if (a < b)
	{
		tmp = a;
		a = b;
		b = tmp;
	}

	for (i = b; i > 0; i--)
	{
		if ((a % i + b % i) == 0)
		{
			ans += 1;
		}
		if (ans == k)
		{
			break;
		}

	}
	printf("%d", i);
	return 0;
}