CF2211C1.Equal Multisets (Easy Version)

This is the easy version of the problem. The difference between the versions is that in this version, the array $ a $ is guaranteed to be a permutation. You can hack only if you solved all versions of this problem.

Given an array $ a $ of size $ n $ , and a parameter $ k $ , an array $ b $ is called cool if the following conditions hold:

• For each $ i $ from $ k $ to $ n $ , the array $ [a_{i-k+1},a_{i-k+2},\ldots,a_i] $ is a rearrangement of $ [b_{i-k+1},b_{i-k+2},\ldots,b_i] $ .

You are given two arrays $ a $ and $ b $ of size $ n $ , and an integer $ k $ . The array $ a $ is guaranteed to be a permutation $ ^{\text{∗}} $ . The array $ b $ only contains integers from $ 1 $ to $ n $ , and $ -1 $ .

Determine if it is possible to replace all $ -1 $ in $ b $ with an integer from $ 1 $ to $ n $ , such that $ b $ is cool with respect to $ k $ .

$ ^{\text{∗}} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in arbitrary order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows.

The first line of each test case contains two integers $ n $ and $ k $ ( $ 1 \leq k \leq n \leq 2\cdot 10^5 $ ).

The second line of each test case contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ 1 \le a_i \le n $ ). In this version, it is guaranteed that each number from $ 1 $ to $ n $ appears exactly once.

The third line of each test case contains $ n $ integers $ b_1,b_2,\ldots,b_n $ ( $ 1 \leq b_i \leq n $ or $ b_i=-1 $ ).

It is guaranteed that the sum of $ n $ across all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, output YES if possible, and NO otherwise. You may print each letter in either uppercase or lowercase.

In the first test case, we have $ k=5 $ . The only subarray of size $ 5 $ is $ [1,5] $ . We can see that $ b $ is a rearrangement of $ a $ , so the answer is YES.

In the second test case, it can be shown that it is impossible to replace all $ -1 $ in $ b $ such that every subarray of size $ k=4 $ are rearrangements of each other.