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Chef got another sequence as a birthday present. He does not like this sequence very much because it is not sorted. Since you are a good programmer, Chef is asking for your help.

You are given a sequence $A_{1}, A_{2}, \ldots, A_{N}$ and an integer $K$. You may perform any number of operations of the following type (in any order): choose a valid integer $i$ and swap $A_{i}$ with $A_{i+K}$. Can you sort the sequence this way?

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains two space-separated integers $N$ and $K$.
The second line contains $N$ space-separated integers $A_{1}, A_{2}, \ldots, A_{N}$.

------ Output ------
For each test case, print a single line containing the string "yes" if the sequence can be sorted or "no" otherwise (without quotes).

------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ K ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{9}$ for each valid $i$
the sum of $N$ over all test cases does not exceed $10^{6}$

------ Subtasks ------
Subtask #1 (50 points): the sequence $A$ is a permutation of the integers $1$ through $N$

Subtask #2 (50 points): original constraints

----- Sample Input 1 ------
2

4 1

1 4 2 3

4 2

1 4 2 3
----- Sample Output 1 ------
yes

no
----- explanation 1 ------
Example case 1: We may freely swap adjacent elements, so the sequence can be sorted e.g. in the following way: $(1, 4, 2, 3) \rightarrow (1, 2, 4, 3) \rightarrow (1, 2, 3, 4)$.

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