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 = map(int, input().split())
    A = list(map(int, input().split()))
    lo = {i: 0 for i in range(2, 2 * k + 1)}

    def update_range(l, r, v):
        if l > r:
            return
        if l == 2:
            lo[r] += v
        else:
            lo[r] += v
            lo[l - 1] -= v

        return

    for i in range(n // 2):
        a1, a2 = A[i], A[n - i - 1]
        m, M = min(a1, a2), max(a1, a2)
        update_range(2, m, 2)
        update_range(m + 1, m + M - 1, 1)
        update_range(m + M + 1, M + k, 1)
        update_range(M + k + 1, 2 * k, 2)


    partial = lo[2 * k]
    answer = partial
    for i in range(2 * k - 1, 1, -1):
        partial += lo[i]
        answer = min(answer, partial)
    print (answer)

t = int(input())
for i in range(t):
    solve()