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: Time Limit Exceeded)

package main

import (
	"fmt"
	"sort"
	"strings"
)

func main() {
	var s string
	var k int
	fmt.Scan(&s, &k)

	l := map[string]struct{}{}
	for start := range s {
		for end := start + 1; end <= len(s); end++ {
			l[s[start:end]] = struct{}{}
		}
	}
	ss := make([]substring, 0)
	for k, _ := range l {
		ss = append(ss, substring{val: k})
	}

	sort.Sort(substrings(ss))
	fmt.Println(ss[k-1].val)
}

type substring struct {
	val string
}

type substrings []substring

func (s substrings) Len() int {
	return len(s)
}

func (s substrings) Less(i, j int) bool {
	if strings.HasPrefix(s[i].val, s[j].val) {
		return false
	}
	for k := range s[i].val {
		if s[i].val[k] == s[j].val[k] {
			continue
		}
		return s[i].val[k] < s[j].val[k]
	}
	return true
}

func (s substrings) Swap(i, j int) {
	s[i], s[j] = s[j], s[i]
}