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 solve(n, k, a):

    maxv = {i: 0 for i in range(2, 2*k+1) }
    minv = {i: 0 for i in range(2, 2*k+1) }
    exactv = {i: 0 for i in range(2, 2*k+1) }

    for i in range(n//2):
        x, y = a[i], a[-1-i]
        x, y = min(x, y), max(x, y)

        exactv[x+y] += 1
        minv[x+1] += 1
        maxv[y+k] += 1

    rs = 0
    for i in range(2, 2*k+1):
        rs += minv[i]
        minv[i] = rs

    rs = 0
    for i in range(2*k, 1, -1):
        rs += maxv[i]
        maxv[i] = rs

    # print(exactv)
    # print(minv)
    # print(maxv)

    return min( [ (n // 2 - minv[i] ) + (n // 2 - maxv[i] ) + (n // 2 - exactv[i]) for i in range(2, 2*k+1) ] )


t = int(input().strip())

for _ in range(t):

    n, k = list(map(int, input().strip().split()))

    a =  list(map(int, input().strip().split()))

    print(solve(n, k, a))