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:
from collections import defaultdict
for i in range(int(input())):
    n,k = map(int, input().split())
    l1 = list(map(int, input().split()))

    sum_array = []
    couple_array = []
    for j in range(len(l1)//2):
        sum_array.append(l1[j] + l1[-j-1])
        couple_array.append((l1[j],l1[-j-1]))

    # hash-map ban gaya idhar
    d = defaultdict(int)
    for ii in sum_array:
        d[ii] += 1

    # range bana loya idhar
    range_array = []
    for ii in couple_array:
        range_array.append([min(ii)+1, max(ii) + k])
    # print(range_array)

    # preff array banauga idhar
    pref_array = [0]*(2*k+2)
    for ii in range_array:
        pref_array[ii[0]] = pref_array[ii[0]] + 1
        pref_array[ii[1]+1] = pref_array[ii[1]+1] - 1
    # print(pref_array)

    # implementing prefix sum array
    for ii in range(1,len(pref_array)):
        pref_array[ii] = pref_array[ii] + pref_array[ii-1]
    # print(pref_array)

    count_array = []
    for ii in range(2,2*k+1):
        if d.get(ii):
            a0 = d.get(ii)
        else:
            a0 = 0
        a1 = pref_array[ii] - a0
        a2 = n//2 - a1 -a0
        count  = 2*a2 + a1
        count_array.append(count)
    print(min(count_array))