CF1073G.Yet Another LCP Problem

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.

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 $\sum\limits_{i = 1}^{i = q}{l_i} \le 2 \cdot 10^5$ .

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

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 $\text{LCP}(\text{abacaba}, \text{abacaba}) + \text{LCP}(\text{abacaba}, \text{aba}) + \text{LCP}(\text{aba}, \text{abacaba}) + \text{LCP}(\text{aba}, \text{aba}) = 7 + 3 + 3 + 3 = 16$ .