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, arr):
    temp = [0 for i in range(0, 2*k + 10)]
    for i in range(0, n//2):
        v1 = arr[i]
        v2 = arr[n - 1 - i]
        # p1 = 2
        p1 = min(v1, v2) + 1
        p2 = v1 + v2
        p3 = max(v1, v2) + k
        # p5 = k + k
        temp[2] += 2
        temp[p1] -= 1
        temp[p2] -= 1
        temp[p2 + 1] += 1
        temp[p3 + 1] += 1
    res = n
    cur = 0
    for i in range(2, 2*k + 1):
        cur += temp[i]
        res = min(cur, res)
    return res



t = int(input())
for i in range(0, t):
    n, k = map(int, input().split())
    arr = list(map(int, input().split()))
    res = solve(n, k, arr)
    print(res)