Problem: 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.

Examples

Input

3 7
at
coder
codar


Output

atcodar


Input

3 7
coder
codar
at


Output

codarat


Input

4 13
kyuri
namida
zzzzzzz
aaaaaa


Output

namidazzzzzzz

Solution (in CPP):

Solution:
//#pragma optimize("Ofast")
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<string>
#include<cstring> 
#include<cassert>
#include<cmath>
#include<sstream>
#include<fstream>
#include<map>
#include<set>
#include<vector>
#include<queue>
#include<stack>
#include<bitset>
using namespace std;
int len[2005];
char s[2005][10005];
bitset<10005> can[2005];
pair<int,int> dp[2][2005];
int main(){
	int n,k;
	cin>>n>>k;
	for(int i=0;i<n;i++){
		scanf("%s",s[i]);
		len[i]=strlen(s[i]);
	}
	for(int i=0;i<n;i++){
		can[i].reset();
	}
	can[n]=1;
	for(int i=n-1;i>=0;i--){
		can[i]=can[i+1]|(can[i+1]<<len[i]);
	}
	int cnt=0,ii=0;
	for(int i=0;i<n;i++){
		if(can[i+1][k-len[i]]) dp[0][cnt++]=make_pair(i,0);
	}
	string res;
	pair<int,int> *a=dp[0],*b=dp[1];
	for(int i=1;i<=k;i++){
		char mi='z';
		int cnt2=0;
		for(int j=0;j<cnt;j++){
			mi=min(s[a[j].first][a[j].second],mi);
		}
		res+=mi;
		int miid=1e9;
		for(int j=0;j<cnt;j++){
			int fi=a[j].first,se=a[j].second;
			if(s[fi][se]==mi){
				if(se+1==len[fi]) miid=min(miid,fi);
				else{
					b[cnt2++]=make_pair(fi,se+1);
				}
			}
		}
		for(int j=miid+1;j<n;j++){
			if(k-len[j]-i>=0&&can[j+1][k-len[j]-i]) b[cnt2++]=make_pair(j,0);
		}
		swap(a,b);
		cnt=cnt2;
	}
	cout<<res;
}