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: Runtime Error)

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <string>
#include <math.h>
#include <stdio.h>
#include <iomanip>
#include <limits>
#include <list>
#include <queue>
#include <tuple>
#include <map>
#include <sstream>
using namespace std;
#define MOD (long long int)(1e9+7)
#define ll long long int
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define reps(i,n) for(int i=1; i<=(int)(n); i++)
#define REP(i,n) for(int i=n-1; i>=0; i--)
#define REPS(i,n) for(int i=n; i>0; i--)
#define FOR(i,a,b) for(int i=a; i<(int)(b); i++)
#define ALL(x) (x).begin(),(x).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define SORT(c) sort(ALL(x))
#define CLR(a) memset((a), 0 ,sizeof(a))
#define PB push_back
#define MP make_pair
#define SP << " " <<
const int INF = 1001001001;
const ll LINF = 100100100100100100;
const double EPS = 1e-10;
const double PI  = acos(-1.0);
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<VI> VVI;

template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val){
    std::fill( (T*)array, (T*)(array+N), val );
}

__attribute__((constructor))
void initial(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(15);
}

signed main(){
  int n,k; cin>>n>>k;
	vector<string> S;
  rep(i,n){
    string s; cin>>s;
    S.PB(s);
  }
  string dp[2005][10005];
  rep(i,2005){
    rep(j,10005){
      dp[i][j] = "{}";
    }
  }
  // memset(dp, '~', sizeof(dp));
  // Fill(dp, "{}");
  rep(i,n){
    int l = S[i].size();
    // dp[i][l] = S[i];
    if(i!=0){
      rep(j,l) dp[i][j] = dp[i-1][j];
      dp[i][l] = min(dp[i-1][l], S[i]);
      for(int j=l+1; j<=k; j++){
        dp[i][j] = min(dp[i-1][j-l]+S[i], dp[i-1][j]);
      }
    }else{
      dp[i][l] = S[i];
    }
  }
  cout << dp[n-1][k] << endl;

  return 0;
}