Chef has an array A of size N and an integer K. He can perform the following operation on A any number of times:
Select any $K distinct indices i_{1}, i_{2}, \ldots, i_{K}$ and increment the array elements at these K indices by 1.
Formally, set A_{i_{j}} := A_{i_{j}} + 1 for all 1 ≤ j ≤ K.

For example, if A = [3, 2, 8, 4, 6] and we select the indices 2, 3, 5, then A becomes [3, 2 + 1, 8 + 1, 4, 6 + 1] i.e. [3, 3, 9, 4, 7].

Determine if Chef can make the array A palindromic by applying the given operation any number of times.

Note: An array is called palindrome if it reads the same backwards and forwards, for e.g. [4, 10, 10, 4] and [7, 1, 7] are palindromic arrays.

------ Input Format ------

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first line of each test case contains two integers N and K — the size of the array A and the parameter mentioned in the statement.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$ denoting the array A.

------ Output Format ------

For each test case, output YES if we can make A palindromic by applying the given operation. Otherwise, output NO.

You may print each character of YES and NO in uppercase or lowercase (for example, yes, yEs, Yes will be considered identical).

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤K ≤N ≤10^{5}$
$1 ≤A_{i} ≤10^{6}$
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$.

----- Sample Input 1 ------
4
5 3
2 4 5 4 2
6 1
4 5 5 4 6 4
6 2
4 5 5 4 6 4
4 2
1 2 3 3

----- Sample Output 1 ------
YES
YES
YES
NO

----- explanation 1 ------
Test case $1$: The given array $A$ is already palindromic.

Test case $2$: We can apply the following operations:
- Select index $[4]$: $A$ becomes $[4, 5, 5, 5, 6, 4]$
- Select index $[2]$: $A$ becomes $[4, 6, 5, 5, 6, 4]$

Test case $3$: We can apply the following operations:
- Select index $[2, 4]$: $A$ becomes $[4, 6, 5, 5, 6, 4]$

Test case $4$: It can be proven that $A$ can not be converted into a palindrome using the given operations.

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