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"
    "bufio"
    "os"
    "strings"
    "strconv"
    "sort"
)

func main() {
    var str string
    stdin := bufio.NewScanner(os.Stdin)

    if stdin.Scan() {
        str = stdin.Text()
        arr := strings.Split(str, " ")
        A, _ := strconv.Atoi(arr[0])
        B, _ := strconv.Atoi(arr[1])
        K, _ := strconv.Atoi(arr[2])
        cnt := 0
        var max int
        var list []int

        if A >= B {
            max = A
        } else {
            max = B
        }

        for i := 1; i <= max; i++ {
            if A % i == 0 && B % i ==0 {
                cnt++
                list = append(list, i)

                if cnt == K + cnt {
                    break
                }
            }
        }

        sort.Sort(sort.Reverse(sort.IntSlice(list)))
        fmt.Println(list[K-1])
    }
}