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 bisect import bisect_left, bisect_right

def solve(arr, k):
    n = len(arr)
    max_val = []
    min_val = []
    cnt = {}
    for i in range(n // 2):
        lhs, rhs = arr[i], arr[n - i - 1]
        if lhs > rhs:
            lhs, rhs = rhs, lhs
        arr[i] = lhs
        arr[n - i - 1] = rhs
        key = lhs + rhs
        cnt.setdefault(key, 0)
        cnt[key] += 1
        max_val.append(k + rhs)
        min_val.append(lhs + 1)
    min_val.sort()
    max_val.sort()


    # print(*arr)
    # print(cnt)
    # print(min_val)
    # print(max_val)
    ans = n
    for x in range(2, 2 * k + 1):
        left_idx = bisect_right(min_val, x)
        right_idx = bisect_left(max_val, x)
        below = n // 2 - left_idx
        above = right_idx
        affect = n // 2 - cnt.get(x, 0)
        candidate = affect + below + above
        # print(x, "->", candidate, ":", cnt.get(x, 0), below, above)
        ans = min(ans, candidate)
    return ans



for _ in range(int(input())):
    n, k = map(int, input().split())
    *arr, = map(int, input().split())
    print(solve(arr, k))