A12547 | Lynyrd Skynyrd

Recently Lynyrd and Skynyrd went to a shop where Lynyrd bought a permutation $p$ of length $n$ , and Skynyrd bought an array $a$ of length $m$ , consisting of integers from $1$ to $n$ .

Lynyrd and Skynyrd became bored, so they asked you $q$ queries, each of which has the following form: "does the subsegment of $a$ from the $l$ -th to the $r$ -th positions, inclusive, have a subsequence that is a cyclic shift of $p$ ?" Please answer the queries.

A permutation of length $n$ is a sequence of $n$ integers such that each integer from $1$ to $n$ appears exactly once in it.

A cyclic shift of a permutation $(p_1, p_2, \ldots, p_n)$ is a permutation $(p_i, p_{i + 1}, \ldots, p_{n}, p_1, p_2, \ldots, p_{i - 1})$ for some $i$ from $1$ to $n$ . For example, a permutation $(2, 1, 3)$ has three distinct cyclic shifts: $(2, 1, 3)$ , $(1, 3, 2)$ , $(3, 2, 1)$ .

A subsequence of a subsegment of array $a$ from the $l$ -th to the $r$ -th positions, inclusive, is a sequence $a_{i_1}, a_{i_2}, \ldots, a_{i_k}$ for some $i_1, i_2, \ldots, i_k$ such that $l \leq i_1 < i_2 < \ldots < i_k \leq r$ .

The first line contains three integers $n$ , $m$ , $q$ ( $1 \le n, m, q \le 2 \cdot 10^5$ ) — the length of the permutation $p$ , the length of the array $a$ and the number of queries.

The next line contains $n$ integers from $1$ to $n$ , where the $i$ -th of them is the $i$ -th element of the permutation. Each integer from $1$ to $n$ appears exactly once.

The next line contains $m$ integers from $1$ to $n$ , the $i$ -th of them is the $i$ -th element of the array $a$ .

The next $q$ lines describe queries. The $i$ -th of these lines contains two integers $l_i$ and $r_i$ ( $1 \le l_i \le r_i \le m$ ), meaning that the $i$ -th query is about the subsegment of the array from the $l_i$ -th to the $r_i$ -th positions, inclusive.

Print a single string of length $q$ , consisting of $0$ and $1$ , the digit on the $i$ -th positions should be $1$ , if the subsegment of array $a$ from the $l_i$ -th to the $r_i$ -th positions, inclusive, contains a subsequence that is a cyclic shift of $p$ , and $0$ otherwise.