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 Counter, defaultdict


def get_by(x):
    c = 0
    for i in range(n // 2):
        if x == a[i] + a[n - 1 - i]:
            continue
        if k + a[n - 1 - i] < x:
            c += 2
        else:
            c += 1
    return c


for _ in range(int(input())):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    c = defaultdict(int)
    original_counter = Counter()
    one_diff_counter = Counter()
    for i in range(n // 2):
        x, y = a[i], a[n - i - 1]
        original_counter[x + y] += 1
        one_diff_counter[min(x, y) + 1] += 1
        one_diff_counter[max(x, y) + k + 1] -= 1

    one_diff = 0
    minimum_change = float('inf')
    for i in range(2, 2 * k + 1):
        zero_diff = original_counter[i]
        one_diff += one_diff_counter[i]
        two_diff = n - zero_diff - one_diff * 2
        change = one_diff + two_diff
        minimum_change = min(minimum_change, change)
    print(minimum_change)