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data structures

string suffix structures

*2600

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G. Yet Another LCP Problem

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet $$$\text{LCP}(s, t)$$$ 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.

Input

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

Output

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

Example

Input

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

Output

13

2

12

16

Note

Description of queries:

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

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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