A14105. 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 $1 \leq p_1 < p_2 < \ldots < p_m \leq n$ , is called beautiful, if $s_{p_i} = t_i$ for all $i$ from $1$ to $m$ . The width of a sequence is defined as $\max\limits_{1 \le i < m} \left(p_{i + 1} - p_i\right)$ .

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.

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.

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

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 $\{1, 2\}$ .