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:
// By Hacheylight

#include <map>
#include <set>
#include <ctime>
#include <queue>
#include <stack>
#include <cmath>
#include <vector>
#include <bitset>
#include <cstdio>
#include <cctype>
#include <string>
#include <numeric>
#include <cstring>
#include <cassert>
#include <climits>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std ;
//#define int long long
#define rep(i, a, b) for (int i = (a); i <= (b); i++)
#define per(i, a, b) for (int i = (a); i >= (b); i--)
#define loop(it, v) for (auto it = v.begin(); it != v.end(); it++)
#define cont(i, x) for (int i = head[x]; i; i = e[i].nxt)
#define clr(a) memset(a, 0, sizeof(a))
#define ass(a, sum) memset(a, sum, sizeof(a))
#define lowbit(x) (x & -x)
#define all(x) x.begin(), x.end()
#define SC(t, x) static_cast <t> (x)
#define ub upper_bound
#define lb lower_bound
#define pqueue priority_queue
#define mp make_pair
#define pb push_back
#define pof pop_front
#define pob pop_back
#define fi first
#define se second
#define y1 y1_
#define Pi acos(-1.0)
#define iv inline void
#define enter cout << endl
#define siz(x) ((int)x.size())
#define file(x) freopen(x".in", "r", stdin),freopen(x".out", "w", stdout)
typedef long double ld ;
typedef long long ll ;
typedef unsigned long long ull ;
typedef pair <int, int> pii ;
typedef pair <ll, int> pli ;
typedef pair<int, pii> tri ;
typedef vector <int> vi ;
typedef vector <pii> vii ;
typedef vector <vi> vvi ;
typedef queue <int> qi ;
typedef queue <pii> qii ;
typedef set <int> si ;
typedef map <int, int> mii ;
typedef map <string, int> msi ;
const int N = 2010 ;
const int M = 10010 ;
const int INF = 0x3f3f3f3f ;
const int iinf = 1 << 30 ;
const ll linf = 2e18 ;
const int mod = 1000000007 ;
const double eps = 1e-7 ;
void douout(double x){ printf("%lf\n", x + 0.0000000001) ; }
template <class T> void print(T a) { cout << a << endl ; exit(0) ; }
template <class T> void chmin(T &a, T b) { if (a > b) a = b ; }
template <class T> void chmax(T &a, T b) { if (a < b) a = b ; }
void add(int &a, int b) { a = a + b < mod ? a + b : a + b - mod ; }
void sub(int &a, int b) { a = (a - b + mod) % mod ; }
void mul(int &a, int b) { a = (ll) a * b % mod ; }
int addv(int a, int b) { return (a += b) >= mod ? a -= mod : a ; }
int subv(int a, int b) { return (a -= b) < 0 ? a += mod : a ; }
int mulv(int a, int b) { return (ll) a * b % mod ; }
int read() {
    int f = 1, x = 0 ;
    char ch = getchar() ;
    while (!isdigit(ch)) { if (ch == '-') f = -1 ; ch = getchar() ; }
    while (isdigit(ch)) { x = x * 10 + ch -'0' ; ch = getchar() ; }
    return x * f ;
}
int pw(int a, int b) {
    int s = 1 ;
    for (; b; b >>= 1, a = (ll) a * a % mod)
    if (b & 1) s = (ll) s * a % mod ;
    return s ;
}

int n, k, len[N], Now, cnt ;
char s[N][M], ans[M] ;
bitset <M> is[N] ;
pii vis[2][M] ; 

int main() {
	scanf("%d%d", &n, &k) ;
	rep(i, 1, n) scanf("%s", s[i] + 1), len[i] = strlen(s[i] + 1) ;
	is[n + 1][0] = 1 ;
	per(i, n, 1) is[i] = is[i + 1] | (is[i + 1] << len[i]) ;
	rep(i, 1, n) if(is[i + 1][k - len[i]]) vis[0][++cnt] = mp(i, 1) ;
	rep(i, 0, k - 1) {
		char c = 'z' ;
		rep(j, 1, cnt) chmin(c, s[vis[Now][j].fi][vis[Now][j].se]) ;
		ans[i] = c ; int tmp = 0, id = n + 1 ;
		rep(j, 1, cnt) {
			int u = vis[Now][j].fi, pos = vis[Now][j].se ;
			if (s[u][pos] != c) continue ;
			if (len[u] == pos) chmin(id, u) ;
			else vis[Now ^ 1][++tmp] = mp(u, pos + 1) ; 
		}
		rep(j, id + 1, n)
		if (k - len[j] - i - 1 >= 0 && is[j + 1][k - len[j] - i - 1])
		vis[Now ^ 1][++tmp] = mp(j, 1) ;
		Now ^= 1, cnt = tmp ;
	}
	printf("%s", ans) ;
	return 0;
}