Stringforces

- 设 $s$ 是一个由前 $k$ 个小写字母构成的字符串，$v$ 是前 $k$ 个小写字母中的某一个。定义 $\mathrm{MaxLen}(s,v)$ 表示 $s$ 所有仅由字母 $v$ 构成的连续子串的最长长度。 - 定义 $s$ 的价值为所有 $\mathrm{MaxLen}(S,v)$ 的最小值，其中 $v$ 取遍前 $k$ 个小写字母。 - 现在给定一个长度为 $n$ 的字符串 $s$，$s$ 中字母要么是前 $k$ 个小写字母中的某一个，要么是问号。你需要将 $s$ 中的每一个问号替换成前 $k$ 个小写字母中的一个，并最大化 $s$ 的价值。方便起见，你只需要输出这个最大的价值即可。 - 保证 $1\leq n\leq 2\times 10^5$，$1\leq k\leq 17$。

You are given a string $ s $ of length $ n $ . Each character is either one of the first $ k $ lowercase Latin letters or a question mark. You are asked to replace every question mark with one of the first $ k $ lowercase Latin letters in such a way that the following value is maximized. Let $ f_i $ be the maximum length substring of string $ s $ , which consists entirely of the $ i $ -th Latin letter. A substring of a string is a contiguous subsequence of that string. If the $ i $ -th letter doesn't appear in a string, then $ f_i $ is equal to $ 0 $ . The value of a string $ s $ is the minimum value among $ f_i $ for all $ i $ from $ 1 $ to $ k $ . What is the maximum value the string can have?

The first line contains two integers $ n $ and $ k $ ( $ 1 \le n \le 2 \cdot 10^5 $ ; $ 1 \le k \le 17 $ ) — the length of the string and the number of first Latin letters used. The second line contains a string $ s $ , consisting of $ n $ characters. Each character is either one of the first $ k $ lowercase Latin letters or a question mark.

Print a single integer — the maximum value of the string after every question mark is replaced with one of the first $ k $ lowercase Latin letters.

10 2
a??ab????b

4

9 4
?????????

2

2 3
??

0

15 3
??b?babbc??b?aa

3

4 4
cabd

1

In the first example the question marks can be replaced in the following way: "aaaababbbb". $ f_1 = 4 $ , $ f_2 = 4 $ , thus the answer is $ 4 $ . Replacing it like this is also possible: "aaaabbbbbb". That way $ f_1 = 4 $ , $ f_2 = 6 $ , however, the minimum of them is still $ 4 $ . In the second example one of the possible strings is "aabbccdda". In the third example at least one letter won't appear in the string, thus, the minimum of values $ f_i $ is always $ 0 $ .