# [USACO12JAN]视频游戏的连击Video Game Combos

## 题目描述

Bessie is playing a video game! In the game, the three letters 'A', 'B', and 'C' are the only valid buttons. Bessie may press the buttons in any order she likes; however, there are only N distinct combos possible (1 <= N <= 20). Combo i is represented as a string S\_i which has a length between 1 and 15 and contains only the letters 'A', 'B', and 'C'.
Whenever Bessie presses a combination of letters that matches with a combo, she gets one point for the combo. Combos may overlap with each other or even finish at the same time! For example if N = 3 and the three possible combos are "ABA", "CB", and "ABACB", and Bessie presses "ABACB", she will end with 3 points. Bessie may score points for a single combo more than once.
Bessie of course wants to earn points as quickly as possible. If she presses exactly K buttons (1 <= K <= 1,000), what is the maximum number of points she can earn?
贝西在玩一款游戏，该游戏只有三个技能键 “A”“B”“C”可用，但这些键可用形成N种(1 <= N<= 20)特定的组合技。第i个组合技用一个长度为1到15的字符串S\_i表示。
当贝西输入的一个字符序列和一个组合技匹配的时候，他将获得1分。特殊的，他输入的一个字符序列有可能同时和若干个组合技匹配，比如N=3时，3种组合技分别为"ABA", "CB", 和"ABACB",若贝西输入"ABACB"，他将获得3分。
若贝西输入恰好K (1 <= K <= 1,000)个字符，他最多能获得多少分？

## 输入输出格式

### 输入格式

\* Line 1: Two space-separated integers: N and K.
\* Lines 2..N+1: Line i+1 contains only the string S\_i, representing combo i.

### 输出格式

\* Line 1: A single integer, the maximum number of points Bessie can obtain.

## 输入输出样例

### 输入样例 #1

```
3 7
ABA
CB
ABACB
```

### 输出样例 #1

```
4
```

## 说明

The optimal sequence of buttons in this case is ABACBCB, which gives 4 points--1 from ABA, 1 from ABACB, and 2 from CB.