C1. Equal Multisets (Easy Version)
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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).

Input

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 $$$2\cdot 10^5$$$.

Output

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

Example
Input
4
5 5
1 2 3 4 5
3 1 5 2 4
5 4
4 1 2 5 3
2 -1 -1 -1 -1
6 4
1 2 4 3 5 6
-1 -1 3 -1 -1 -1
6 4
1 2 4 3 5 6
-1 -1 3 3 -1 -1
Output
YES
NO
YES
NO
Note

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.