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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class C
{
	public static void Main()
	{	
		string s = Console.ReadLine();
		int K = Int32.Parse(Console.ReadLine());

		Dictionary<string,bool> dict = 
			new Dictionary<string,bool>(s.Length * s.Length);
		for(int i = 1; i <= s.Length; i++)
		{
			for(int j = 0; j <= s.Length - i; j++)
			{
				string str = s.Substring(j,i);  // start:j, length:i
				if(!dict.ContainsKey(str))
					dict[str] = true;
			}
		}

		List<string> list = new List<string>(s.Length * s.Length);
		foreach(string key in dict.Keys)
			list.Add(key);
		list.Sort();
		Console.WriteLine(list[K-1]); 
	}	
}