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 alg (int x, int y) {
	if (x % y == 0) {
		return y;
	}
	else {
		alg(y, x % y);
	}
}
int main(void) {
	int a, b, k, memo;
	int ans[100];
	scanf("%d %d %d", &a, &b, &k);
	if (a < b) {
		memo = b;
		b = a;
		a = memo;
	}

	ans[0]=alg(a, b);
	int n = 0;
	for (int i = ans[0]-1; i  ; --i) {
		if (a % i == 0 && b % i == 0) {
			ans[++n] = i;
		}
	}
	printf("%d", ans[k - 1]);

	return 0;
}