Problem:
Score : 300 points

Problem Statement

You are given a string s.
Among the different substrings of s, print the K-th lexicographically smallest one.

A substring of s is a string obtained by taking out a non-empty contiguous part in s.
For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.
Also, we say that substrings are different when they are different as strings.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

1 ≤ |s| ≤ 5000

s consists of lowercase English letters.

1 ≤ K ≤ 5

s has at least K different substrings.

Partial Score

200 points will be awarded as a partial score for passing the test set satisfying |s| ≤ 50.

Input

Input is given from Standard Input in the following format:

s
K

Output

Print the K-th lexicographically smallest substring of K.

Sample Input 1

aba
4

Sample Output 1

b

s has five substrings: a, b, ab, ba and aba.
Among them, we should print the fourth smallest one, b.
Note that we do not count a twice.

Sample Input 2

atcoderandatcodeer
5

Sample Output 2

andat

Sample Input 3

z
1

Sample Output 3

z

Solution in Go (1.6) (judge verdict: Accepted)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func nextString() string {
	if !sc.Scan() {
		panic("failed scan string")
	}
	return sc.Text()
}

func nextInt() int {
	if !sc.Scan() {
		panic("failed scan int")
	}
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc.Split(bufio.ScanWords)

	s := nextString()
	k := nextInt()

	subs := make([]string, k)

	for i := 0; i < len(s); i++ {
		for j := i + 1; j < len(s)+1; j++ {
			sub := s[i:j]

			for l := 0; l < k; l++ {
				if sub == subs[l] {
					// dup
					break
				}
				if subs[l] == "" {
					subs[l] = sub
					break
				}
				if sub < subs[l] {
					if l != k-1 {
						copy(subs[l+1:], subs[l:])
					}
					subs[l] = sub
					break
				}
			}

		}
	}

	fmt.Println(subs[k-1])
}