Legen...

给定 $n$ 个字符串 $S_i$ 和正整数数列 $a_i$（$S_i$ 可能相同）。 定义一个字符串 $T$ 的**价值**为 $$\sum_{i=1}^n \mathrm{count}(T;S_i)\cdot a_i$$ 其中 $\mathrm{count}(T;S_i)$ 表示 $S_i$ 在 $T$ 中的出现次数，例如 $\mathrm{count}(\texttt{aaab},\texttt{aa})=2$。 欲构造一个长度为 $l$ 的字符串，最大化其价值。输出最大价值。 字符集是小写英文字母。$1\le n\le 200$，$1\le l\le 10^{14}$，$1\le \sum |S_i|\le 200$，$1\le a_i\le 100$。 $\text{Statement fixed by @Starrykiller.}$

Barney was hanging out with Nora for a while and now he thinks he may have feelings for her. Barney wants to send her a cheesy text message and wants to make her as happy as possible. Initially, happiness level of Nora is $ 0 $ . Nora loves some pickup lines like "I'm falling for you" and stuff. Totally, she knows $ n $ pickup lines, each consisting only of lowercase English letters, also some of them may be equal (in writing, but different in pronouncing or meaning though). Every time Nora sees $ i $ -th pickup line as a consecutive subsequence of Barney's text message her happiness level increases by $ a_{i} $ . These substrings may overlap, for example, Nora will see the pickup line aa twice and the pickup line ab once in text message aaab. Due to texting app limits, Barney's text may have up to $ l $ characters. Barney asked you to help him make Nora as much happy as possible, it's gonna be legen...

The first line of input contains two integers $ n $ and $ l $ ( $ 1<=n<=200,1<=l<=10^{14} $ ) — the number of pickup lines and the maximum length of Barney's text. The second line contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=100 $ ), meaning that Nora's happiness level increases by $ a_{i} $ after every time seeing $ i $ -th pickup line. The next $ n $ lines contain the pickup lines. $ i $ -th of them contains a single string $ s_{i} $ consisting of only English lowercase letter. Summary length of all pickup lines does not exceed $ 200 $ . All strings are not empty.

Print the only integer — the maximum possible value of Nora's happiness level after reading Barney's text.

3 6
3 2 1
heart
earth
art

6

3 6
3 2 8
heart
earth
art

16

An optimal answer for the first sample case is hearth containing each pickup line exactly once. An optimal answer for the second sample case is artart.