题目描述

Mikaeel has got $n$ strings named $s_{1}, \ldots, s_{n}$ each consists of lower-case English letters. He wants to pick a non-empty substring of each one and concatenate them together to make a final string of size $k$. Help Mikaeel create the smallest lexicographical string possible.

输入格式

In the first line, you are given two integers $n$ and $k$, the number of strings and the size of the final string, respectively.

The $n$ following lines contain the sequence $s_{1}, \ldots, s_{n}$, the strings of Mikaeel.

输出格式

In a single line, print the smallest lexicographical string achievable.

3 5
abc
xxx
aaa

abcxa

5 6
ab
bz
zb
aa
cb

abbaab

提示

Constraints

• $n, \sum_{i=1}^{n}\left|s_{i}\right| \leq 4000$
• $n \leq k \leq \sum_{i=1}^{n}\left|s_{i}\right|$

Subtasks