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 JAVA):

Solution:
 /**
 * @author egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict
 * @url
 * @category
 * @date
 **/

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;

public class CF1343D {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int T = parseInt(in.readLine());
        for (int t = 0; t < T; t++) {
            StringTokenizer st = new StringTokenizer(in.readLine());
            int N = parseInt(st.nextToken()), K = parseInt(st.nextToken());
            int[] values = new int[N];
            int[][] ranges = new int[N / 2][];
            st = new StringTokenizer(in.readLine());
            for (int i = 0; i < N; i++)
                values[i] = parseInt(st.nextToken());
            int[] sums = new int[2 * K + 1];
            for (int i = 0; i < N / 2; i++) {
                ranges[i] = new int[]{Math.min(values[i], values[N - i - 1]) + 1, Math.max(values[i], values[N - i - 1]) + K};
                sums[values[i] + values[N - i - 1]]++;
            }
            int[] arr = f(2 * K + 1, ranges);
            int min = N;
            for (int x = 0; x < arr.length; x++) {
               min = Math.min(min, 2 * (N / 2 - arr[x]) + arr[x] - sums[x]);
            }
            System.out.println(min);
        }
    }

    static int[] f(int N, int[][] ranges) {
        int[] beginRange = new int[N];
        int[] endRange = new int[N];
        int[] result = new int[N];
        for (int[] range : ranges) {
            beginRange[range[0]]++;
            endRange[range[1]]++;
        }
        for (int i = 0; i < N; i++) {
            if (i > 0)
                result[i] = result[i - 1] + beginRange[i] - endRange[i - 1];
            else
                result[i] = beginRange[i] - endRange[i];
        }
        return result;
    }
}