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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"os"
)

func min(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}

func main() {
	var a, b, num, k int
	fmt.Scan(&a, &b, &k)
	lim := min(a, b)
	for i := lim; i >= 1; i-- {
		if a%i == 0 && b%i == 0 {
			num++
			if num == k {
				fmt.Println(i)
				os.Exit(0)
			}
		}
	}
}