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: Runtime Error)

using System;
using System.Collections;
using System.Linq;
namespace ARC097
{
    class Program
    {
        static string alp = "abcdefghijklmnopqrstuvwxyz";
        static void Main()
        {
            //以下入力を受け取る
            string s = Console.ReadLine();
            int k = int.Parse(Console.ReadLine());

            //以下処理内容
            ArrayList sub = new ArrayList();

            int index = 0;
            for (; ; )
            {
                for (int i = 0; i < s.Length; i++)
                {
                    if (alp[index] != s[i])
                        continue;
                    for (int j = 1; j <= s.Length - i; j++)
                        sub.Add(s.Substring(i, j));
                }
                index++;
                if (sub.Count >= k)
                    break;
                if (index == alp.Length)
                    break;
            }


            string[] sub2 = (string[])sub.ToArray(typeof(string));
            Array.Sort(sub2);

            ArrayList sub3 = new ArrayList();
            sub3.Add(sub2[0]);
            for (int i = 1; i < sub2.Length; i++)
                if (sub2[i - 1] != sub2[i])
                    sub3.Add(sub2[i]);

            //for (int i = 0; i < sub2.Length; i++)
            //    Console.WriteLine(sub2[i]);

            //以下解答を出力
            Console.WriteLine((string)sub3[k - 1]);
        }
    }
}