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:
// This amazing code is by Eric Sunli Chen.
#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <utility>
#include <vector>
using namespace std;
template<typename T> void get_int(T &x)
{
	char t=getchar();
	bool neg=false;
	x=0;
	for(; (t>'9'||t<'0')&&t!='-'; t=getchar());
	if(t=='-')neg=true,t=getchar();
	for(; t<='9'&&t>='0'; t=getchar())x=x*10+t-'0';
	if(neg)x=-x;
}
template<typename T> void print_int(T x)
{
	if(x<0)putchar('-'),x=-x;
	short a[20]= {},sz=0;
	while(x>0)a[sz++]=x%10,x/=10;
	if(sz==0)putchar('0');
	for(int i=sz-1; i>=0; i--)putchar('0'+a[i]);
}
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define get1(a) get_int(a)
#define get2(a,b) get1(a),get1(b)
#define get3(a,b,c) get1(a),get2(b,c)
#define printendl(a) print_int(a),puts("")
typedef long long LL;
typedef unsigned long long uLL;
typedef pair<int,int> pii;
const int inf=0x3f3f3f3f;
const LL Linf=1ll<<61;
const double pi=acos(-1.0);

const int magic=2000;

char s[2111][10111];
int n,k,l[2111];
bool dp[2111][10111];
vector<pii> pos,npos;
int main()
{
	get2(n,k);
	for(int i=1;i<=n;i++)
	{
		scanf("%s",s[i]+1);
		l[i]=strlen(s[i]+1);
	}
	dp[n+1][0]=1;
	for(int i=n;i>=1;i--)
	{
		for(int j=0;j<=k;j++)
		{
			dp[i][j]=dp[i+1][j];
			if(j>=l[i])dp[i][j]|=dp[i+1][j-l[i]];
		}
	}
	for(int i=1;i<=n;i++)if(dp[i+1][k-l[i]])pos.pb(mp(i,1));
	for(int _=1;_<=k;_++)
	{
		npos.clear();
		char cur='z';for(int i=0;i<(int)pos.size();i++)cur=min(cur,s[pos[i].ff][pos[i].ss]);
		putchar(cur);
		
		int mn=n;
		for(int i=0;i<(int)pos.size();i++)
		{
			if(s[pos[i].ff][pos[i].ss]!=cur)continue;
			if(l[pos[i].ff]==pos[i].ss)
				mn=min(mn,pos[i].ff);
			else npos.pb(mp(pos[i].ff,pos[i].ss+1));
		}
		for(int i=mn+1;i<=n;i++)if(_+l[i]<=k&&dp[i+1][k-_-l[i]])npos.pb(mp(i,1));
		if((int)npos.size()>magic)
		{
			random_shuffle(npos.begin(),npos.end());
			npos.resize(magic);
		}
		
		pos.swap(npos);
	}
	return 0;
}