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.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //[summary]C - K-th Substring
            string s = Console.ReadLine();
            int k = int.Parse(Console.ReadLine());

            //文字列を1文字ずつに分解して、辞書順に並べた後、K番目までを取得
            //(それ以降は考慮する必要がない)
            var chars = GetCharacters(s).OrderBy(x => x.C).Take(k).ToList();

            //K番目と思われるsubstringをリストアップ
            var substrings = new List<string>();

            for(int i = 0; i < chars.Count; i++)
            {
                int index = chars[i].Index;

                for(int j = 1; j <= k; j++)
                {
                    if (index + j <= s.Length)
                    {
                        var substring = s.Substring(index, j);
                        substrings.Add(substring);
                    }
                }
            }

            var result = substrings.Distinct().OrderBy(x => x).ToList();
            Console.WriteLine(result[k - 1]);
        }

        static IEnumerable<Character> GetCharacters(string s)
        {
            for(int i = 0; i < s.Length; i++)
            {
                yield return new Character(s[i], i);
            }
        }
    }

    struct Character
    {
        public char C { set; get; }
        public int Index { set; get; }

        public Character(char c, int index)
        {
            C = c;
            Index = index;
        }
    }
}