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:
from collections import defaultdict
from itertools import accumulate

def solve(a, n, k):
    pairs = [(min(x, y), max(x, y)) for x, y in zip(a[:n], a[::-1][:n])]

    # print(f'{pairs=}')

    one_change = [(x+1, y+k) for x, y in pairs]
    # print(f'{one_change=}')

    changes = [0] * (2*k+ 2)
    for a, b in one_change:
        # print(f'{b=}')
        changes[a] += 1
        changes[b+1] -= 1

    changes = list(accumulate(changes))
    # print(f'{changes=}')

    for x, y in pairs:
        changes[x+y] += 1
    # print(changes[2:2*k+1])
    print(2*n - max(changes[2:2*k+1]))
    # print('============')
    
for _ in range(int(input())):
    n, k = map(int, input().split())

    a = list(map(int, input().split()))

    solve(a, n//2, k)

# n, k = 8, 7
# a = [6, 1, 1, 7, 6, 3, 4, 6]

# solve(a, n//2, k)