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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
using namespace std;
int main(int argc, char* argv[])
{
	int N,K;
	cin>>N>>K;
	vector<string> s(N,"");
	vector<string> S;
	int i,j;
	for (i=0;i<N;i++){
		cin>>s[i];
	}
	string minS;
	string tmpS;
	for (i=0;i<N-1;i++){
		for (j=i+1;j<N;j++){
			if (s[i].length()+s[j].length()==K){
				tmpS = s[i]+s[j];
				if (minS=="" || minS.compare(tmpS)>0){
					minS=s[i]+s[j];
				}
			}
		}
	}
	cout<<minS<<endl;
	return 0;
}