CF1203D2.Remove the Substring (hard version)

The only difference between easy and hard versions is the length of the string.

You are given a string $s$ and a string $t$, both consisting only of lowercase Latin letters. It is guaranteed that $t$ can be obtained from $s$ by removing some (possibly, zero) number of characters (not necessary contiguous) from $s$ without changing order of remaining characters (in other words, it is guaranteed that $t$ is a subsequence of $s$).

For example, the strings "test", "tst", "tt", "et" and "" are subsequences of the string "test". But the strings "tset", "se", "contest" are not subsequences of the string "test".

You want to remove some substring (contiguous subsequence) from $s$ of maximum possible length such that after removing this substring $t$ will remain a subsequence of $s$.

If you want to remove the substring $s[l;r]$ then the string $s$ will be transformed to $s_1 s_2 \dots s_{l-1} s_{r+1} s_{r+2} \dots s_{|s|-1} s_{|s|}$ (where $|s|$ is the length of $s$).

Your task is to find the maximum possible length of the substring you can remove so that $t$ is still a subsequence of $s$.

简单版本与困难版本的唯一区别在于字符串的长度。

给你两个字符串 $s$ 和 $t$，它们均由小写拉丁字母组成。保证 $t$ 可通过从 $s$ 中删除若干（可能为零）个字符（不必连续）并保持剩余字符的相对顺序得到（即：保证 $t$ 是 $s$ 的一个子序列）。

例如，字符串 "test"、"tst"、"tt"、"et" 和 "" 都是 "test" 的子序列；但 "tset"、"se" 和 "contest" 不是 "test" 的子序列。

你希望从 $s$ 中删除一个长度尽可能大的子串（即一段连续的子序列），使得删除后 $t$ 仍然是 $s$ 的子序列。

若你要删除子串 $s[l;r]$，则字符串 $s$ 将变为 $s_1 s_2 \dots s_{l-1} s_{r+1} s_{r+2} \dots s_{|s|-1} s_{|s|}$（其中 $|s|$ 表示 $s$ 的长度）。

你的任务是：求出可删除的子串的最大可能长度，使得 $t$ 在删除后仍为 $s$ 的子序列。

The first line of the input contains one string $s$ consisting of at least $1$ and at most $2 \cdot 10^5$ lowercase Latin letters.

The second line of the input contains one string $t$ consisting of at least $1$ and at most $2 \cdot 10^5$ lowercase Latin letters.

It is guaranteed that $t$ is a subsequence of $s$.

输入的第一行包含一个字符串 $s$，由至少 $1$ 个、至多 $2 \cdot 10^5$ 个小写拉丁字母组成。

输入的第二行包含一个字符串 $t$，由至少 $1$ 个、至多 $2 \cdot 10^5$ 个小写拉丁字母组成。

保证 $t$ 是 $s$ 的一个子序列。

Print one integer — the maximum possible length of the substring you can remove so that $t$ is still a subsequence of $s$.

输出一个整数——你可以删除的子串的最大可能长度，使得 $t$ 仍然是 $s$ 的子序列。