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;

class AtCoder
{
    static void Main(string[] args)
    {
        Scanner cin = new Scanner();
        string s = Console.ReadLine();
        int K = cin.Int();

        List<string> x = new List<string>();
        for(int i = 1; i <= K; i++)
        {
            for(int j = 0; j < s.Length - i + 1; j++)
            {
                x.Add(s.Substring(j, i));
            }
        }

        string[] ans = x.OrderBy(t => t).ToArray();
        Console.WriteLine(ans[K - 1]);

        Console.ReadLine();
    }

    static void Swap<T>(ref T a, ref T b)
    {
        T tmp = a;
        a = b;
        b = tmp;
    }

    static long BinarySearch<T>(T[] array, T target) where T : IComparable<T> //2分探索
    {
        int min = 0;
        int max = array.Length - 1;

        while (true)
        {
            // 範囲内に見つからなかった
            if (max < min) return -1;
            // 範囲内の中央値と比較する
            int mid = min + (max - min) / 2;
            switch (target.CompareTo(array[mid]))
            {
                case -1:    // 中央値より小さい
                    max = mid - 1;
                    break;
                case 1:     // 中央値より大きい
                    min = mid + 1;
                    break;
                case 0:     // 見つかった
                    return mid;
            }
        }
    }
}

class Scanner //標準入力
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string Next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return Next();
        i = 0;
        return s[i++];
    }

    public int Int()
    {
        return int.Parse(Next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = Int() + add;
        }
        return Array;
    }

    public long Long()
    {
        return long.Parse(Next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = Long() + add;
        }
        return Array;
    }

    public double Double()
    {
        return double.Parse(Next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = Double() + add;
        }
        return Array;
    }
}