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:
import io
import os

from collections import Counter, defaultdict, deque

# Python can't sort tuples efficiently...
def tup(a, b):
    if b == -1:
        return a * 2 + 0
    return a * 2 + 1


def untup(t):
    a, b = divmod(t, 2)
    if b == 0:
        b = -1
    return a, b


def solve(N, K, A):
    cost = N
    best = N
    points = []
    for i in range(N // 2):
        j = N - 1 - i
        x = A[i]
        y = A[j]
        if x > y:
            x, y = y, x
        lo = x + 1  # replace y with 1
        hi = min(y + K, 2 * K)  # replace x with k

        points.append(tup(lo, -1))
        points.append(tup(x + y, -1))
        points.append(tup(x + y, +1))
        points.append(tup(hi, +1))
    points.sort()
    for t in points:
        _, delta = untup(t)
        cost += delta
        best = min(best, cost)
    return best


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    T = int(input())
    for t in range(T):
        N, K = [int(x) for x in input().split()]
        A = [int(x) for x in input().split()]
        ans = solve(N, K, A)
        print(ans)