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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	line := nextLine()
	parts := strings.Split(line, " ")
	a, _ := strconv.Atoi(parts[0])
	b, _ := strconv.Atoi(parts[1])
	k, _ := strconv.Atoi(parts[2])

	ret := make([]int, 0)
	for i := 1; i < 101; i++ {
		if a%i == 0 && b%i == 0 {
			ret = append(ret, i)
		}
	}

	fmt.Println(ret[len(ret)-k])
}