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(0,t):
    n,k=map(int,input().split())
    l1=list(map(int,input().split()))
    l2 = [0] * (2*k+2)
    d = {}
    for y in range(0, n // 2):
        l = min(l1[y], l1[n - y - 1]) + 1
        r = max(l1[y], l1[n - y - 1]) + k
        l2[l] += 1
        l2[r+1] -= 1
        sum = l1[y] + l1[n - y - 1]
        if sum in d.keys():
            d[sum] += 1
        else:
            d[sum] = 1
    l1=[l2[0]]
    for y in range(1,len(l2)):
        l1.append(l1[-1]+l2[y])#l1 is prefix array
    m=10000000
    for j in range(2,2*k+1):
        a=0
        c=0
        if j in d.keys():
            a=d[j]
        b=l1[j]-a
        c=n//2-b-a
        if b+2*c<m:
            m=b+(2*c)
    print(m)