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: Time Limit Exceeded)

#include <iostream>
#include <cstring>
#include <cstdio>
#define ll long long
#define rg register
using namespace std;

inline int read(){
	int sum=0,f=1;char c=getchar();
	while(c>'9'||c<'0'){if(c=='-') f=-1;c=getchar();}
	while(c<='9'&&c>='0'){sum=sum*10+c-'0';c=getchar();}
	return f*sum;
}

const int N=100005;
int n,K;
string s[N],f[N];

signed main(){
	freopen("test.out","r",stdin);
	n=read();K=read();
	for(rg int i=1;i<=n;i++) cin>>s[i];
	for(rg int i=1;i<=n;i++){
		int l=s[i].size();
		for(rg int j=K;j>l;j--){
			if(f[j-l].empty()) continue;
			if(f[j].empty()) f[j]=f[j-l]+s[i];
			else{
				if(f[j]<f[j-l]) continue;
				f[j]=min(f[j],f[j-l]+s[i]);
			}
		}
		if(f[l].empty()) f[l]=s[i];
		f[l]=min(f[l],s[i]);
	}
	cout<<f[K]<<endl;
	return 0;
}