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,stdout
for query in range(int(stdin.readline())):
  nk=stdin.readline().split()
  n=int(nk[0])
  k=int(nk[1])
  a=[int(x) for x in stdin.readline().split()]
  mylist=[0]*2*k
  b=[]
  for x in range(n//2):
    b.append([a[x],a[n-x-1]])
  for x in b:
    mylist[1]+=2
    mylist[min(x)]-=1
    mylist[sum(x)-1]-=1
    if sum(x)<2*k:
      mylist[sum(x)]+=1
    if max(x)+k<2*k:
      mylist[max(x)+k]+=1
  for x in range(1,2*k):
    mylist[x]+=mylist[x-1]
  c=min(mylist[1:])
  stdout.write(str(c)+'\n')