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:
t = int(input())
from collections import defaultdict
import math
for _ in range(t):
    n, k = list(map(int, input().split()))
    seq = list(map(int, input().split()))

    prefix_arr = [0]*(2*k+10)
    zero_count = defaultdict(int)
    for i in range(n//2):
        zero_count[seq[i] + seq[n-i-1]] += 1

        a, b = sorted((seq[i], seq[n-i-1]))

        L = a + 1
        R = b + k

        prefix_arr[L] += 1
        prefix_arr[R+1] -= 1
        
    prefsum = 0
    for i in range(2*k + 10):
        prefsum +=  prefix_arr[i]
        prefix_arr[i] = prefsum
    
    ans = n
    for i in range(2, 2*k + 1):
        zero = zero_count[i]
        ones = prefix_arr[i] - zero
        twos = n//2 - ones - zero

        total = ones + twos*2
        ans = min(ans, total)
        
    print(ans)