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 main():
    from collections import Counter
    from itertools import accumulate
    T = int(input())
    for _ in range(T):
        N, K = (int(i) for i in input().split())
        A = [int(i) for i in input().split()]

        c = Counter()
        for i in range(N//2):
            c[A[i] + A[-(i+1)]] += 1
        S = [0]*(2*K+5)
        for i in range(N//2):
            mi = min(A[i], A[-(i+1)]) + 1
            ma = max(A[i], A[-(i+1)]) + K
            S[mi] += 1
            S[ma + 1] -= 1
        S = list(accumulate(S))
        ans = 3*10**5
        for x in range(2, 2*K+1):
            cur = (S[x] - c[x]) + (N//2 - S[x])*2
            ans = min(ans, cur)
        print(ans)


if __name__ == '__main__':
    main()