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.Diagnostics;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main()
    {
        string s = Console.ReadLine();
        int K = int.Parse(Console.ReadLine());
        // Console.WriteLine(UsingList(s, K));
        Console.WriteLine(UsingHashSetOrderBy(s, K));
        // Console.WriteLine(UsingSortedSet(s, K));
    }

    // List→IEnumerable→IOrderedEnumerable
    static string UsingList(string s, int K)
    {
        List<string> list = new List<string>();
        for (int len = 1; len <= Math.Min(s.Length, 5); len++)
        {
            for (int i = 0; i <= s.Length - len; i++)
            {
                list.Add(s.Substring(i, len));
            }
        }
        var list_d = list.Distinct();
        var ranking = list_d.OrderBy(i => i);
        return ranking.ElementAt(K - 1);
    }

    // HashSet→IOrderedEnumerable
    static string UsingHashSetOrderBy(string s, int K)
    {
        HashSet<string> hs = new HashSet<string>();
        for (int len = 1; len <= Math.Min(s.Length, 5); len++)
        {
            for (int i = 0; i <= s.Length - len; i++)
            {
                hs.Add(s.Substring(i, len));
            }
        }
        var ranking = hs.OrderBy(i => i);
        return ranking.ElementAt(K - 1);
    }

    // SortedSetのみ！
    static string UsingSortedSet(string s, int K)
    {
        SortedSet<string> ss = new SortedSet<string>();
        for (int len = 1; len <= Math.Min(s.Length, 5); len++)
        {
            for (int i = 0; i <= s.Length - len; i++)
            {
                ss.Add(s.Substring(i, len));
            }
        }
        return ss.ElementAt(K - 1);
    }
}