Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in PYTHON3):

Solution:
def task(n, k, a):
    sums = {}
    maxk = k * 2 + 2
    mins = [0] * maxk
    maxs = [0] * maxk

    half = int(n / 2)

    for i in range(0, half):
        c = a[i]
        d = a[n - 1 - i]
        suma = c + d

        if not suma in sums:
            sums[suma] = 0

        sums[suma] += 1

        mins[min(c, d) + 1] += 1
        maxs[max(c, d) + k + 1] += 1

    value = 0
    best = half

    for i in range(0, maxk):
        value += mins[i] - maxs[i]
        if i in sums:
            one_swap = value - sums[i]
            two_swaps = half - value
            swaps = one_swap + 2 * two_swaps
            best = min(best, swaps)

    print(best)


t = int(input())
for i in range(0, t):
    n, k = list(map(int, input().split()))
    a = list(map(int, input().split()))
    task(n, k, a)