B. Lynyrd Skynyrdtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputRecently 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.InputThe 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.OutputPrint 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.ExamplesInput3 6 32 1 31 2 3 1 2 31 52 63 5Output110Input2 4 32 11 1 2 21 22 33 4Output010NoteIn the first example the segment from the 1-st to the 5-th positions is 1, 2, 3, 1, 2. There is a subsequence 1, 3, 2 that is a cyclic shift of the permutation. The subsegment from the 2-nd to the 6-th positions also contains a subsequence 2, 1, 3 that is equal to the permutation. The subsegment from the 3-rd to the 5-th positions is 3, 1, 2, there is only one subsequence of length 3 (3, 1, 2), but it is not a cyclic shift of the permutation.In the second example the possible cyclic shifts are 1, 2 and 2, 1. The subsegment from the 1-st to the 2-nd positions is 1, 1, its subsequences are not cyclic shifts of the permutation. The subsegment from the 2-nd to the 3-rd positions is 1, 2, it coincides with the permutation. The subsegment from the 3 to the 4 positions is 2, 2, its subsequences are not cyclic shifts of the permutation.
Input3 6 32 1 31 2 3 1 2 31 52 63 5
Output110
['data structures', 'dfs and similar', 'dp', 'math', 'trees', '*2000']