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 bisect import bisect_left
from collections import Counter


def solve(n, k, a):
    s = [a[i] + a[n-i-1] for i in range(n//2)]
    amin    = sorted([min(a[i], a[n-i-1]) for i in range(n//2)])
    amax    = sorted([max(a[i], a[n-i-1]) for i in range(n//2)])
    ans     = float('inf')
    counter = Counter(s)
    for v in range(2*k+1):
        count  = n//2 - bisect_left(amin, v)
        count1 = bisect_left(amax, v-k)
        count2 = n//2 - count - count1
        count3 = counter[v]
        ans    = min(ans, (count+count1)*2 + count2 - count3)
    return ans



def main():
    tc = int(input())
    inp = lambda: [int(x) for x in input().split()]
    for _ in range(tc):
        n, k = inp()
        a = inp()
        print(solve(n, k, a))


if __name__ == '__main__':
    main()