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:
from sys import stdin


def inp():
    return stdin.buffer.readline().rstrip().decode("utf8")


def itg():
    return int(stdin.buffer.readline())


def mpint():
    return map(int, stdin.buffer.readline().split())

from collections import defaultdict

def segment_count(segments):
    d = defaultdict(int)
    for start, end in segments:
        d[start] += 1
        d[end + 1] -= 1
    coordinate = sorted(d.keys())
    counts = [0]
    for key in coordinate:
        counts.append(counts[-1] + d[key])
    return coordinate, counts

for case in range(itg()):
    n, k = mpint()
    arr = tuple(mpint())
    cnt = [0] * (2*k + 7)
    cnt[0] = n
    seg = []
    for i in range(n >> 1):
        a, b = arr[i], arr[-i-1]
        mn = min(a, b) + 1
        mx = max(a, b) + k
        # [mn,a+b): -1, a+b:-2, (a+b,mx]:-1
        # -> [mn,a+b], [a+b,mx]
        seg.extend([(mn, a+b), (a+b, mx)])

    print(n - max(segment_count(seg)[1]))