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.

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.

Equal Multisets (Easy Version)

Examples