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

t = int(input())

for _ in range(t):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    d = defaultdict(int)

    cumsum = [0 for i in range(2 * k + 1)]
    cumsum_max = [0 for i in range(2 * k + 1)]
    for i in range(n // 2):
        d[a[i] + a[n - i - 1]] += 1
        cumsum[min(a[i], a[n - i - 1])] += 1
        if max(a[i], a[n - i - 1]) + k + 1 < 2 * k + 1:
            cumsum_max[max(a[i], a[n - i - 1]) + k + 1] += 1

    for i in range(len(cumsum) - 2, 0, -1):
        cumsum[i] += cumsum[i + 1]

    for i in range(1, len(cumsum_max)):
        cumsum_max[i] += cumsum_max[i - 1]

    ans = -1

    for i in range(2, 2 * k + 1):
        pair_count = d[i]
        pair_sum = i
        change = n // 2 - pair_count + cumsum[pair_sum] + cumsum_max[pair_sum]
        ans = change if ans < 0 else min(ans, change)
    print(ans)