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 sys
t=int(input())
for i in range(t):
    n,k=map(int,input().split())
    arr=list(map(int,input().split()))
    cnt=[0 for i in range((2*k)+1)]
    for j in range(n//2):
        cnt[arr[j]+arr[n-j-1]]+=1
    pref=[0 for j in range((2*k)+2)]
    for j in range(0,n//2):
        l1=1+arr[j]
        l2=1+arr[n-j-1]
        r1=arr[j]+k
        r2=arr[n-j-1]+k
        if(max(l1,l2)>min(r1,r2)):
            continue
        pref[min(l1,l2)]+=1
        pref[max(r1,r2)+1]-=1
    for j in range(1,2*k+2):
        pref[j]+=pref[j-1]
    ans=sys.maxsize
    for j in range(2,2*k+1):
        ans=min(ans,((pref[j]-cnt[j])+((n//2-pref[j])*2)))
    print(ans)