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 itertools import accumulate

### TEMPLATE <<<
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return (map(int,input().split()))
### TEMPLATE >>>

def sgn(x):
    if x>0:
        return '+'
    else:
        return '-'

def solve(n, k, a):
    h = [0] * (2*k + 5)
 #   print(h)
    for i in range(n//2):
        j = n - i - 1
        h[0] += 2;
        h[min(a[i], a[j]) + 1] -= 1
        h[a[i] + a[j]] -= 1
        h[a[i] + a[j] + 1] += 1
        h[max(a[i], a[j]) + k + 1] += 1

    pref = list(accumulate(h))
    return min(pref)

def main():
    T = int(input())
    for tt in range(T):
        n, k = invr()
        a = list(invr())
        print(solve(n, k, a))
main()