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:
import collections
import operator
if __name__ == "__main__":
    n =  int(input())
    for i in range(n):
        mk = [int(i) for i in input().split(' ')]
        m = mk[0]
        k = mk[1]
        ll = [int(i) for i in input().split(' ')]

        rr = [0]*(2*k + 2)
        pref = [0]*(2*k + 2)
        lt = [0]*(2*k + 2)

        for i in range(m//2):
            rr[ll[i] + ll[m-1-i]] += 1

        for i in range(m//2):
            a = min(ll[i] + 1, ll[m-1-i] + 1)
            b = max(ll[i] + k, ll[m-i-1] + k) + 1
            pref[a] += 1
            pref[b] -= 1

        for i in range(1, 2*k +1):
            pref[i] += pref[i-1]

        ans = m
        for i in range(2, 2*k + 1):
            ans = min(ans, pref[i] - rr[i] + (m//2 - pref[i])*2)

        print(ans)