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:
#this solution is a translation of MikeMirzayanov's
#c++ editorial solution 

def run(lst, n, k):
 
    ans = float("inf")

    cnt = [0 for i in range(int(2*k + 1))]

    for i in range(int(n/2)):
        soma = lst[i] + lst[n - i - 1]
        cnt[soma] += 1

    # print(cnt)

    pref = [0 for i in range(int(2*k + 2))]
    for i in range(int(n/2)):
        menor = min(lst[i] + 1, lst[n - i - 1] + 1)
        maior = max(lst[i] + k, lst[n - i - 1] + k)

        pref[menor] += 1
        pref[maior+1] -= 1

    # print(pref)

    for i in range(1, len(pref)-1):
        pref[i] += pref[i - 1]
    for i in range(1, len(pref) -1):
        pref[i] = n - cnt[i] - pref[i]

    print(min(pref[2:-1]))

i = int(input())
for _ in range(i):
    n, k = map(int, input().split())
    lst = list(map(int, input().split()))
    run(lst, n, k)