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: Runtime Error)

package main

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

func main() {
	nextReader = NewScanner()
	line1 := nextInt()
	a := line1[0]
	b := line1[1]
	k := line1[2]

	var arr []int
	n := max([]int{a, b}...)
	for i := 1; i < n; i++ {
		if a%i == 0 && b%i == 0 {
			arr = append(arr, i)
		}
	}
	fmt.Println(arr[k-1])
}

// ------ Mathライブラリ ---------------------------------//
func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}

func maxIdx(a ...int) int {
	r := a[0]
	index := 0
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
			index = i
		}
	}
	return index
}

func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}

func minIdx(a ...int) int {
	r := a[0]
	index := 0
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
			index = i
		}
	}
	return index
}

func sum(a []int) (r int) {
	for i := range a {
		r += a[i]
	}
	return r
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// ------ Mathライブラリ ---------------------------------//

// ----- 標準入力用の関数 ----------------------------------//
var nextReader func() []string

func NewScanner() func() []string {
	r := bufio.NewScanner(os.Stdin)
	r.Buffer(make([]byte, 1024), int(1e+11))
	return func() []string {
		r.Scan()
		return strings.Fields(r.Text())
	}
}

func nextString() []string {
	return nextReader()
}

func nextInt() []int {
	var intArray []int
	strArray := nextReader()
	for _, v := range strArray {
		i, _ := strconv.Atoi(v)
		intArray = append(intArray, i)
	}
	return intArray
}

func nextFloat64() []float64 {
	var floatArray []float64
	strArray := nextReader()
	for _, v := range strArray {
		f, _ := strconv.ParseFloat(v, 64)
		floatArray = append(floatArray, f)
	}
	return floatArray
}

// ------ 標準入力用の関数 ---------------------------------//

// ------ あまり使わない -----------------------------------//
func nextInt64() []int64 {
	var int64Array []int64
	strArray := nextReader()
	for _, v := range strArray {
		i, _ := strconv.ParseInt(v, 10, 64)
		int64Array = append(int64Array, i)
	}
	return int64Array
}

// ------ あまり使わない -----------------------------------//