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:
#include<iostream>
#include<bitset>
#include<cstring>
#include<algorithm>
using namespace std;

int len[2010], n, k, cnt, ncnt;
char s[2010][10010], ans[1000010];
bitset<10010> can[2010];
pair<int, int> vis[2][10010];

int main()
{
	scanf("%d%d", &n, &k);
	for (int i = 1; i <= n; i++) scanf("%s", s[i]), len[i] = strlen(s[i]);
	can[n + 1][0] = 1;
	for (int i = n; i >= 1; i--) can[i] = can[i + 1] | (can[i + 1] << len[i]);
	for (int i = 1; i <= n; i++) if (can[i + 1][k - len[i]]) vis[0][++cnt] = make_pair(i, 0);
	int ii = 0;
	for (int i = 0; i < k; i++)
	{
		char minc = 'z';
		for (int j = 1; j <= cnt; j++) minc = min(minc, s[vis[ii][j].first][vis[ii][j].second]);
		ans[i] = minc;
		int minid = n + 1;
		ncnt = 0;
		for (int j = 1; j <= cnt; j++)
		{
			int nid = vis[ii][j].first, nlen = vis[ii][j].second;
			if (s[nid][nlen] != minc)
				continue;
			if (nlen + 1 == len[nid])
				minid = min(minid, nid);
			else
				vis[ii ^ 1][++ncnt] = make_pair(nid, nlen + 1);
		}
		for (int j = minid + 1; j <= n; j++)
			if (k - len[j] - i - 1 >= 0 && can[j + 1][k - len[j] - i - 1])
				vis[ii ^ 1][++ncnt] = make_pair(j, 0);
		ii ^= 1;
		cnt = ncnt;
	}
	printf("%s", ans);
}