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:
import java.util.*;
import java.io.*;

public class Solution {
    static FastReader in;
    static PrintWriter out;
    
    static int a[] = new int[422222];
    static int b[] = new int[422222];
    static int c[] = new int[422222];
    
    public static void main(String args[]) throws FileNotFoundException, InterruptedException
    {
        in = new FastReader(System.in);
        out = new PrintWriter(System.out);
        int t = in.nextInt();
        while(t -- > 0)
        {
            int n = in.nextInt();
            int k = in.nextInt();
            for(int i = 0; i <= k + k + 2; i ++)
                    c[i] = b[i] = 0;
            for(int i = 1; i <= n; i ++)
            {
                a[i] = in.nextInt();
            }
            for(int i = 1; i <= n/2; i ++)
            {
                c[a[i] + a[n - i + 1]] ++;
                int x = a[i], y = a[n - i + 1];
                int l = 0, r = 0;
                if(x > y)
                {
                    l = 1 + y;
                    r = x + k;
                }
                else
                {
                    l = x + 1;
                    r = y + k;
                }
                b[l] ++;
                b[r + 1] --;
            }
            int s = 0, ans = 111111111;
            for(int i = 2; i <= 2*k; i ++)
            {
                b[i] += b[i - 1];
                int q = (b[i] - c[i]) + 2*(n/2 - (b[i]));
                ans = Math.min(ans, q);
            }
            out.println(ans);
        }
        
        
        out.close();
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }
 
        Integer nextInt() {
            return Integer.parseInt(next());
        }
 
        Long nextLong() {
            return Long.parseLong(next());
        }
 
        Double nextDouble() {
            return Double.parseDouble(next());
        }
 
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }
 
        String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }
    }
}