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 _ in range(t):
    n,k=map(int, input().strip().split())
    arr=list(map(int, input().strip().split()))

    raj=dict()
    
    rang=[]
    for i in range(n//2):
        if(raj.get(arr[i]+arr[n-i-1])==None):
            raj[arr[i]+arr[n-i-1]]=1
        else:
            raj[arr[i]+arr[n-i-1]]+=1
        rang.append( (min(arr[i],arr[n-i-1])+1, max(arr[i],arr[n-i-1])+k))

    pre=[0]*((k*2)+2)
    for i in rang:
        pre[i[0]]+=1
        pre[i[1]+1]-=1
    for i in range(1,len(pre)):
        pre[i]=pre[i]+pre[i-1]

    
    ans=float('inf')
    for i in range(2,(k*2) + 1):
        cnt=0
        
        zero=0
        if(raj.get(i)!=None):
            zero=raj[i]

        one=pre[i]-zero
        two=n//2-one-zero

        cnt=(one) + ((two)*2)
        ans=min(ans,cnt)
    print(ans)