Note: The only difference between this chapter and chapter 2 is that here, all card values are guaranteed to be distinct and only up to (N).
Let's cut to the chase. You have a deck of (N) face-up cards, each displaying a unique integer between (1) and (N).
Cutting the deck once consists of taking a stack of between (1) and (N - 1) (inclusive) cards from the top and moving it to the bottom in the same order. For example, for the deck ([5, 1, 2, 4, 3]) ordered from top to bottom, cutting (2) cards from the top would yield ([2, 4, 3, 5, 1]):
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Initially, the (i)th card from the top is (A_i). Is it possible to cut the deck exactly (K) times to reorder the deck such that the (i)th card from the top is (B_i) for all (i)?
Constraints
(1 \le T \le 200) (2 \le N \le 500{,}000) (0 \le K \le 10^9) (1 \le A_i, B_i \le N) (A) and (B) are each permutations of (1..N).
The sum of (N) across all test cases is at most (5{,}000{,}000).
Input Format
Input begins with an integer (T), the number of test cases. For each test case, there is first a line containing two space-separated integers (N) and (K). Then, there is a line containing (N) space-separated integers, (A_1, ..., A_N). Then, there is a line containing (N) space-separated integers, (B_1, ..., B_N).
Output Format
For the (i)th test case, print "Case #i: " followed by "YES" if it's possible to cut the deck (K) times to change the deck from (A_i) to (B_i), or "NO" otherwise.
Sample Explanation
In the first case, it's possible to get to the new order with (K = 1) cut (cutting 2 cards from the top).
In the second case, it's impossible to change ([3, 1, 4, 2]) to ([1, 2, 3, 4]) with any number of cuts.
In the third case, it's impossible for the deck to be in a different order after (K = 0) cuts.