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;

class Program
{
    static void Main()
    {
        string s = Console.ReadLine();
        int k = int.Parse(Console.ReadLine());
        int n = s.Length;
        Dictionary<string, int> dic = new Dictionary<string, int>();


        Console.WriteLine(String.CompareOrdinal("a", "b"));
        Console.WriteLine(String.CompareOrdinal("b", "a"));
        Console.WriteLine(String.CompareOrdinal("a", "a"));

        Console.WriteLine(String.CompareOrdinal("a", "at"));
        Console.WriteLine(String.CompareOrdinal("at", "a"));
        Console.WriteLine(String.CompareOrdinal("at", "at"));


        for (int i = 0; i < n; i++)
        {
            for(int j = 1; i + j <= n; j++)
            {
                dic[s.Substring(i, j)] = 0;
            }
        }
        string[] keys = dic.Keys.ToArray();
        int len = keys.Length;

        for (int i = 0; i < k; i++)
        {
            for (int j = i + 1; j < len; j++)
            {
                if(String.CompareOrdinal(keys[i], keys[j]) > 0)
                {
                    string tmp = keys[i];
                    keys[i] = keys[j];
                    keys[j] = tmp;
                }
            }
        }

        Console.WriteLine(keys[k - 1]);
    }

}