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 System.Text;

namespace Practice
{
    class Program
    {
        private static int ReadAndParseInt()
        {
            return int.Parse(Console.ReadLine());
        }
        private static int[] ReadAndParseIntArr()
        {
            return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        }
        private static long ReadAndParseLong()
        {
            return long.Parse(Console.ReadLine());
        }
        private static long[] ReadAndParseLongArr()
        {
            return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        }
        static void Main(string[] args)
        {
            SolveA(args);
            //SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }

        static void SolveA(string[] args)
        {
            string s = Console.ReadLine();
            int k = ReadAndParseInt();
            HashSet<string> hash = new HashSet<string>();
            hash.Add(s);

            List<char> candidates = new List<char>();
            for(int c= (int)'a'; c<=(int)'z';++c)
            {
                for(int i=0;i<s.Length;++i)
                {
                    if(s[i] == c)
                    {
                        candidates.Add(s[i]);
                        break;
                    }
                }
                if(candidates.Count >= k)
                {
                    break;
                }
            }

            // 候補charを基準に部分文字列を追加していく
            foreach(char c in candidates)
            {
                for(int i=0;i<s.Length;++i)
                {
                    if(s[i] == c)
                    {
                        // 部分文字列は高々k
                        int maxLen = Math.Min(5, s.Length - i);
                        for (int len = 1; len <= maxLen; ++len)
                        {
                            string sz = s.Substring(i, len);
                            if (!hash.Contains(sz))
                            {
                                hash.Add(sz);
                            }
                        }
                    }
                }
            }

            List<string> list = new List<string>(hash);
            list.Sort();
            string ans = list[k-1];
            Console.WriteLine(ans);
         }
    }
}