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:
def RA():
    l = input().split()
    return [int(s) for s in l]

def solve():
    n, k = RA()
    arr = RA()
    scores = [[0, 0, 0] for i in range(2 * k + 1)]
    for i in range(n // 2):
        a = arr[i]
        b = arr[n - i - 1]
        mini = min(a, b) + 1
        maxi = a + b + k - min(a, b)
        scores[mini][0] += 1
        scores[a + b][1] += 1
        scores[maxi][2] += 1
    needChange = n
    best = needChange
    for i in range(2, 2 * k + 1):
        needChange -= scores[i][0]
        best = min(best, needChange - scores[i][1])
        needChange += scores[i][2]
    print(best)
        
t = int(input())
for i in range(t):
    solve()