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 bsl(n, m, num):
    left = -1
    right = n
    while right - left > 1:
        middle = (left + right) // 2
        if m[middle] >= num:
            right = middle
        else:
            left = middle
    return right


def bsr(n, m, num):
    left = -1
    right = n
    while right - left > 1:
        middle = (left + right) // 2
        if m[middle] > num:
            right = middle
        else:
            left = middle
    return left


def count(n, num, max1, min1):
    ans = 0
    ans += (2 * (n - bsr(n, min1, num) - 1))
    ans += (2 * (bsl(n, max1, num)))
    ans += (n - cs[num] - ans // 2)
    return ans


for j in range(int(input())):
    n, k = map(int,input().split())
    a = list(map(int,input().split()))

    s = list()
    ss = list()
    sw = set()
    cs = dict()
    max1 = list()
    min1 = list()
    for i in range(n // 2):
        max1.append(max(a[i], a[n - i - 1]) + k)
        min1.append(min(a[i], a[n - i - 1]) + 1)
        xxx = a[i] + a[n - i - 1]
        if xxx not in sw:
            sw.add(xxx)
            s.append(xxx)
            cs[xxx] = 1
        else:
            cs[xxx] += 1
        ss.append(xxx)
    max1.sort()
    min1.sort()
    ss.sort()
    n //= 2

    ans = float("inf")
    for suma in s:
        #print(count(n, suma, max1, min1))
        #print(cs[suma])
        ans = min(ans, count(n, suma, max1, min1))

    if min1[-1] <= max1[0]:
        ans = min(ans, n)

    #print(max1)
    #print(min1)
    print(ans)