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 pal(n, k, a):
    zeros = [0 for i in range(2*k+1)]
    ones_prefix = [0 for i in range(2*k+2)]
    for i in range(n//2):
        f, b = a[i], a[n-i-1]
        ones_prefix[min(f+1, b+1)] += 1
        ones_prefix[max(f+k+1, b+k+1)] += -1
        zeros[f+b] += 1
    ones = [0 for i in range(2*k+2)]
    cs = 0
    for i in range(2*k+2):
        cs += ones_prefix[i]
        ones[i] = cs
    best = 2*n
    #print(zeros, ones)
    for i in range(2, 2*k+1):
        zero = zeros[i]
        one = ones[i] - zero
        two = n//2 - zero - one
        changes = one + 2*two
        if changes < best:
            best = changes
    print(best)

t = int(input())
for i in range(t):
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    pal(n, k, a)