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 gcd(a, b int) int {
	if b > a {
		a, b = b, a
	}
	for {
		r := a % b
		if r == 0 {
			return b
		}
		a = b
		b = r
	}
}

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

	r := gcd(a, b)
	for i := r; i > 0; i-- {
		if r%i == 0 {
			k--
		}
		if k == 0 {
			fmt.Println(i)
			break
		}
	}
}