CF1492C.Maximum width

Your classmate, whom you do not like because he is boring, but whom you respect for his intellect, has two strings: $s$ of length $n$ and $t$ of length $m$.

A sequence $p_1, p_2, \ldots, p_m$, where $1 \leq p_1 \lt p_2 \lt \ldots \lt p_m \leq n$, is called beautiful, if $s_{p_i} = t_i$ for all $i$ from $1$ to $m$. The width of a sequence is defined as $\max\limits_{1 \le i \lt m} \left(p_{i + 1} - p_i\right)$.

Please help your classmate to identify the beautiful sequence with the maximum width. Your classmate promised you that for the given strings $s$ and $t$ there is at least one beautiful sequence.

你的同学——你不喜欢他，因为他很无聊，但又敬佩他的才智——有两个字符串：长度为 $n$ 的字符串 $s$ 和长度为 $m$ 的字符串 $t$。

一个序列 $p_1, p_2, \ldots, p_m$，满足 $1 \leq p_1 \lt p_2 \lt \ldots \lt p_m \leq n$，被称为优美的，当且仅当对所有 $i = 1$ 到 $m$，均有 $s_{p_i} = t_i$。该序列的宽度定义为 $\max\limits_{1 \le i \lt m} \left(p_{i + 1} - p_i\right)$。

请帮你的同学找出宽度最大的优美序列。你的同学向你保证：对于给定的字符串 $s$ 和 $t$，至少存在一个优美序列。

The first input line contains two integers $n$ and $m$ ($2 \leq m \leq n \leq 2 \cdot 10^5$) — the lengths of the strings $s$ and $t$.

The following line contains a single string $s$ of length $n$, consisting of lowercase letters of the Latin alphabet.

The last line contains a single string $t$ of length $m$, consisting of lowercase letters of the Latin alphabet.

It is guaranteed that there is at least one beautiful sequence for the given strings.

第一行输入包含两个整数 $n$ 和 $m$（$2 \leq m \leq n \leq 2 \cdot 10^5$），分别表示字符串 $s$ 和 $t$ 的长度。

接下来一行包含一个长度为 $n$ 的字符串 $s$，由小写拉丁字母组成。

最后一行包含一个长度为 $m$ 的字符串 $t$，由小写拉丁字母组成。

保证对于给定的字符串，至少存在一个优美的序列。

Output one integer — the maximum width of a beautiful sequence.

输出一个整数——美丽序列的最大宽度。

In the first example there are two beautiful sequences of width $3$: they are ${1, 2, 5}$ and ${1, 4, 5}$.

In the second example the beautiful sequence with the maximum width is ${1, 5}$.

In the third example there is exactly one beautiful sequence — it is ${1, 2, 3, 4, 5}$.

In the fourth example there is exactly one beautiful sequence — it is ${1, 2}$.

在第一个例子中，有两个宽度为 $3$ 的优美序列：${1, 2, 5}$ 和 ${1, 4, 5}$。

在第二个例子中，宽度最大的优美序列为 ${1, 5}$。

在第三个例子中，恰好存在一个优美序列：${1, 2, 3, 4, 5}$。

在第四个例子中，恰好存在一个优美序列：${1, 2}$。