Statement : C1. Equal Multisets (Easy Version)

C1. 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).

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

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.