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

n = int(input())

for i in range(n):
    m, k = map(int, input().split())
    nums = list(map(int, input().split()))

    #All of the sums: 0 changes
    h = defaultdict(int)
    pair = []
    s, e = 0, len(nums) - 1

    #Two-pointer Algorithm to store all pairs and store all sums in hashmap
    while s < e:
        h[nums[s] + nums[e]] += 1
        pair.append((min(nums[s], nums[e]), max(nums[s], nums[e])))
        s += 1
        e -= 1

    #Prefix Sum ALgorithm
    p = [0] * ((2 * k) + 1)
    for s, e in pair:
        new_range = (s + 1, e + k)
        p[new_range[0]] += 1
        if new_range[1] + 1 < len(p):
            p[new_range[1] + 1] -= 1

    #Prefix sum of all ranges: 1 change
    for i in range(1, len(p)):
        p[i] += p[i - 1]

    final = []

    
    for i in range(2, (2*k) + 1):
        changes = len(pair)
        
        zero, one, two = 0, 0, 0
        if i in h:
            zero += h[i]
            changes -= zero

        if changes:
            one = p[i] - zero
            changes -= one

        if changes:
            two = changes
        final.append(2 * two + one)
        

    print(min(final))