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())
for i in range(t):
    n,k=list(map(int,input().split()))
    arr=list(map(int,input().split()))
    if n==2:
        print(0)
    else:
        count=[0]*(2*k)
        for j in range(n//2):
            count[arr[j]+arr[-j-1]-1]+=1
        pref=[0]*(2*k)
        for j in range(n//2):
            x1=arr[j]+1
            x2=arr[-j-1]+1
            y1=arr[j]+k
            y2=arr[-j-1]+k
            pref[min(x1,x2)-1]+=1
            if max(y1,y2)<(2*k):
                pref[max(y1,y2)]-=1
        for j in range(1,2*k):
            pref[j]+=pref[j-1]
        ans=n//2
        for j in range(1,2*k):
            temp=(pref[j]-count[j])+(2*((n//2)-pref[j]))
            ans=min(ans,temp)
        print(ans)