Yet Another LCP Problem

题面翻译

记$lcp(i,j)$表示i这个后缀和j这个后缀的最长公共前缀长度

给定一个字符串，每次询问的时候给出两个正整数集合A和B,求

$\sum_{i \in A,j \in B}lcp(i,j)$ 的值

题目描述

Let $\text{LCP}(s, t)$ be the length of the longest common prefix of strings $s$ and $t$ . Also let $s[x \dots y]$ be the substring of $s$ from index $x$ to index $y$ (inclusive). For example, if $s =$ "abcde", then $s[1 \dots 3] =$ "abc", $s[2 \dots 5] =$ "bcde".

You are given a string $s$ of length $n$ and $q$ queries. Each query is a pair of integer sets $a_1, a_2, \dots, a_k$ and $b_1, b_2, \dots, b_l$ . Calculate $ \sum\limits_{i = 1}^{i = k} \sum\limits_{j = 1}^{j = l}{\text{LCP}(s[a_i \dots n], s[b_j \dots n])} $ for each query.

输入格式

The first line contains two integers $n$ and $q$ ( $1 \le n, q \le 2 \cdot 10^5$ ) — the length of string $s$ and the number of queries, respectively.

The second line contains a string $s$ consisting of lowercase Latin letters ( $|s| = n$ ).

Next $3q$ lines contains descriptions of queries — three lines per query. The first line of each query contains two integers $k_i$ and $l_i$ ( $1 \le k_i, l_i \le n$ ) — sizes of sets $a$ and $b$ respectively.

The second line of each query contains $k_i$ integers $a_1, a_2, \dots a_{k_i}$ ( $1 \le a_1 < a_2 < \dots < a_{k_i} \le n$ ) — set $a$ .

The third line of each query contains $l_i$ integers $b_1, b_2, \dots b_{l_i}$ ( $1 \le b_1 < b_2 < \dots < b_{l_i} \le n$ ) — set $b$ .

It is guaranteed that $ \sum\limits_{i = 1}^{i = q}{k_i} \le 2 \cdot 10^5 $ and $ \sum\limits_{i = 1}^{i = q}{l_i} \le 2 \cdot 10^5 $ .

输出格式

Print $q$ integers — answers for the queries in the same order queries are given in the input.

样例 #1

样例输入 #1

7 4
abacaba
2 2
1 2
1 2
3 1
1 2 3
7
1 7
1
1 2 3 4 5 6 7
2 2
1 5
1 5

样例输出 #1

13
2
12
16

提示

Description of queries:

1. In the first query $s[1 \dots 7] = \text{abacaba}$ and $s[2 \dots 7] = \text{bacaba}$ are considered. The answer for the query is $ \text{LCP}(\text{abacaba}, \text{abacaba}) + \text{LCP}(\text{abacaba}, \text{bacaba}) + \text{LCP}(\text{bacaba}, \text{abacaba}) + \text{LCP}(\text{bacaba}, \text{bacaba}) = 7 + 0 + 0 + 6 = 13 $ .
2. In the second query $s[1 \dots 7] = \text{abacaba}$ , $s[2 \dots 7] = \text{bacaba}$ , $s[3 \dots 7] = \text{acaba}$ and $s[7 \dots 7] = \text{a}$ are considered. The answer for the query is $ \text{LCP}(\text{abacaba}, \text{a}) + \text{LCP}(\text{bacaba}, \text{a}) + \text{LCP}(\text{acaba}, \text{a}) = 1 + 0 + 1 = 2 $ .
3. In the third query $s[1 \dots 7] = \text{abacaba}$ are compared with all suffixes. The answer is the sum of non-zero values: $ \text{LCP}(\text{abacaba}, \text{abacaba}) + \text{LCP}(\text{abacaba}, \text{acaba}) + \text{LCP}(\text{abacaba}, \text{aba}) + \text{LCP}(\text{abacaba}, \text{a}) = 7 + 1 + 3 + 1 = 12 $ .
4. In the fourth query $s[1 \dots 7] = \text{abacaba}$ and $s[5 \dots 7] = \text{aba}$ are considered. The answer for the query is $ \text{LCP}(\text{abacaba}, \text{abacaba}) + \text{LCP}(\text{abacaba}, \text{aba}) + \text{LCP}(\text{aba}, \text{abacaba}) + \text{LCP}(\text{aba}, \text{aba}) = 7 + 3 + 3 + 3 = 16 $ .