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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Int32;

class Program
{
    static void Main(string[] args)
    {
        label:
        var text = ReadLine();
        int k = Parse(ReadLine()) - 1;
        var result = new List<string>();
        hoge(text, "", null, result);
        WriteLine(result[k]);
    }

    static void hoge(string text, string sub, List<int> kouho, List<string> result)
    {
        var nextList = new SortedList<char, List<int>>();
        if (kouho == null)
        {
            for (int i = 0; i < text.Length; ++i)
            {
                AddNext(text[i], i, nextList, text.Length);
            }
        }
        else
        {
            foreach (int i in kouho)
            {
                if (i + 1 < text.Length)
                {
                    AddNext(text[i + 1], i + 1, nextList, text.Length);
                }
            }
        }
        foreach (var pair in nextList)
        {
            string sub2 = sub + pair.Key.ToString();
            result.Add(sub2);
            if (5 <= result.Count) return;
            hoge(text, sub2, pair.Value, result);
            if (5 <= result.Count) return;
        }
    }

    static void AddNext(char c, int i, SortedList<char, List<int>> list, int capa)
    {
        if (list.ContainsKey(c)) list[c].Add(i);
        else
        {
            if (list.Count == 3)
            {
                var max = list.Keys.Max();
                if (max < c) return;
                else list.Remove(max);
            }
            list[c] = new List<int>(capa) { i };
        }
    }
}