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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

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

func gcd(a, b int) int {
	if b == 0 {
		return a
	}

	return gcd(b, a%b)
}

func main() {
	sc.Split(bufio.ScanWords)
	var slice []int

	a, b, k := read(), read(), read()
	var aint, bint, kint int
	aint, _ = strconv.Atoi(a) //文字列から１０進整数への変換
	bint, _ = strconv.Atoi(b)
	kint, _ = strconv.Atoi(k)

	num := gcd(aint, bint) //最大公約数

	for i := 1; i <= num; i++ {
		if num%i == 0 {
			slice = append(slice, i)
		}
	}
	// fmt.Println(slice)
	// fmt.Println(gcd(aint, bint))
	fmt.Println(slice[kint-1])

}