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=map(int,input().split())
    b=list(map(int,input().split()))
    a=b[:int(n//2)]
    c=b[int(n//2):]
    c.reverse()
    d=[0]*(2*k+2)
    f=dict()
    for j in range(1,2*k+1):
        f[j]=0

    for j in range(n//2):
        r=a[j]+c[j]
        f[r]+=1


        x=min(a[j],c[j])+1
        y=max(a[j],c[j])+k
        d[x]+=1
        d[y+1]-=1
    for i in range(1, 2 * k + 2):
        d[i] += d[i - 1]
    m=100000000000000000
    for j in range(1,2*k+1):
        h=d[j]-f[j]+(int(n//2)-d[j])*2
        m=min(m,h)
    print(m)