Stringforces
Description
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.
Input
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.
Output
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.
Samples
10 2
a??ab????b
4
9 4
?????????
2
2 3
??
0
15 3
??b?babbc??b?aa
3
4 4
cabd
1
Note
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 $0$.