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"

func main() {
	var a, b, k int
	fmt.Scan(&a, &b, &k)
	fmt.Println(divisor(a, b, k))
}

func divisor(a, b, k int) int {
	var i int
	if a > b {
		i = b
	} else {
		i = a
	}
	var count int
	for {
		if a%i == 0 && b%i == 0 {
			count++
		}
		if count == k {
			return i
		}
		i--
	}
}