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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var s = ReadLine();
            var N = s.Length;
            var K = Sarray()[0];
            var mins = new List<char>();
            mins.Add(s.Min());
            IEnumerable<char> enu;
            for (var i = 1; i < 5; ++i)
            {
                enu = s.Where(w => w != mins[i - 1]);
                if (enu.Count() == 0)
                    break;
                mins.Add(enu.Min());
            }
            var kouho = new List<string>();
            var kouhoCount = 0L;
            foreach (var m in mins)
            {
                for (var i = 0; i < N; ++i)
                {
                    if (s[i] == m)
                    {
                        var num = 5;
                        num = Min(num, N - i);
                        kouho.Add(s.Substring(i, num));
                        kouhoCount += num;
                    }
                }
                if (5 < kouhoCount)
                    break;
            }
            kouho.Sort(StringComparer.OrdinalIgnoreCase);
            var hs = new HashSet<string>();
            foreach(var k in kouho)
            {
                for(var i=0;i<k.Length;++i)
                {
                    var ss = k.Substring(0, i + 1);
                    if (!hs.Contains(ss)) hs.Add(ss);
                    if(hs.Count==K)
                    {
                        WriteLine(ss);
                        return;
                    }
                }
            }
            //Out.Flush();
        }
    }
}