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

    cnt_zero = [0] * (2 * k + 5)
    cnt_zero_or_one = [0] * (2 * k + 5)
    i, j = 0, n-1
    while i < j:
        # Without changing any
        actual_sum = a[i] + a[j] 
        cnt_zero[actual_sum] += 1
        # Minimum sum by changing one, i.e keep the smaller and convert the bigger to 1
        min_sum = min(a[i], a[j]) + 1
        # Maximum sum by changing one, i.e keep the bigger and convert the smaller to k
        max_sum = max(a[i], a[j]) + k
        # We can create all possible sum form min to max using a[i] and a[j]
        cnt_zero_or_one[min_sum] += 1
        cnt_zero_or_one[max_sum + 1] -= 1 
        i += 1
        j -= 1
    
    for i in range(1, len(cnt_zero_or_one)):
        cnt_zero_or_one[i] += cnt_zero_or_one[i-1]
    
    ans = 2**31
    for x in range(2, len(cnt_zero_or_one)):
        cnt_one_only = cnt_zero_or_one[x] - cnt_zero[x]
        cnt_two = n / 2 - cnt_zero_or_one[x]
        ans = min(ans, cnt_one_only + cnt_two * 2)

    print(int(ans))