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:
def solve():
    n, k = [int(i) for i in input().split()]
    v = [int(i) for i in input().split()]
    sum = [0] * (2*k + 2)
    
    for i in range(n // 2):
        x = v[i]
        y = v[n - i - 1]
        
        if y > x:
            x, y = y, x
            
        sum[x + y] += 1
        sum[x + k + 1] -= 1
        
        sum[y + 1] += 1
        sum[x + y + 1] -= 1
    pos = -1
    mx = -9999999
    for i in range(len(sum)):
        sum[i] += sum[i - 1]
        if sum[i] > mx:
            mx = sum[i]
            pos = i
            
    elem = pos
    c = 0
    
    for i in range(n//2):
        x = v[i]
        y = v[n - i - 1]
        
        if y > x:
            x, y = y, x
            
        if elem >= y + 1 and elem <= x + k:
            if x + y != elem:
                c += 1
        else :
            c += 2
    
    print(c)


t = int(input())
while t:
    t -= 1
    solve()