Problem:
Score : 1500 points

Problem Statement

Iroha has a sequence of N strings s_1, s_2, ..., s_N.

She will choose some (possibly all) strings from the sequence, then concatenate those strings retaining the relative order, to produce a long string.

Among all strings of length K that she can produce in this way, find the lexicographically smallest one.

Constraints

1 ≦ N ≦ 2000

1 ≦ K ≦ 10^4

For each i, 1 ≦ |s_i| ≦ K.

|s_1| + |s_2| + ... + |s_N| ≦ 10^6

For each i, s_i consists of lowercase letters.

There exists at least one string of length K that Iroha can produce.

Input

The input is given from Standard Input in the following format:

N K
s_1
s_2
:
s_N

Output

Print the lexicographically smallest string of length K that Iroha can produce.

Sample Input 1

3 7
at
coder
codar

Sample Output 1

atcodar

at and codar should be chosen.

Sample Input 2

3 7
coder
codar
at

Sample Output 2

codarat

codar and at should be chosen.

Sample Input 3

4 13
kyuri
namida
zzzzzzz
aaaaaa

Sample Output 3

namidazzzzzzz

namida and zzzzzzz should be chosen.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.io.*;
import java.util.*;

class Solution{
    int N;
    int K;
    String[] strings;

    String answer = "";

    void recurse(int index,String current){
        //System.out.println(current);

        if(current.length() == K){
            if(current.compareTo(answer) < 0 || answer.length() == 0) {
                answer = current;
            }
            
        }

        if(index >= N){
            return ; 
        }

        recurse(index+1,current+strings[index]);
        recurse(index+1,current);

    }


    void solve() throws IOException{
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));

        String[] input = bufferedReader.readLine().split(" ");
        
        N = Integer.parseInt(input[0]);
        K = Integer.parseInt(input[1]);

        strings = new String[N];

        for(int i=0;i<N;i++){
            strings[i] = bufferedReader.readLine();
        }

        recurse(0,"");

        System.out.println(answer);

    }


}

public class Main {

    public static void main(String[] args) throws IOException{

        new Solution().solve();

    }

}