Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class F {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }
    static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }

    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
        int t = ri();
//        int t=1;
        while (t-- > 0)
        {
            int n=ri();
            int[] arr=rai(n);
            List<Integer> list=new ArrayList<>();
            for(int i:arr)
            {
                list.add(i);
            }
            List<Integer> res=new ArrayList<>();
            HashSet<Integer> set=new HashSet<>();
            for(int i=0;i<n-2;i++)
            {
                int min=Integer.MAX_VALUE;
                int ind=-1;
                for(int j=i;j<n;j++)
                {
                    if(list.get(j)<min && !set.contains(list.get(j)))
                    {
                        min=list.get(j);
                        ind=j;

                    }
                }
//                System.out.println(i+" "+ind);
                if(ind==-1)
                {
                    continue;
                }

                set.add(list.get(ind));

                if(ind!=i)
                {
                    while(ind-i>2)
                    {
                        int val=list.remove(ind);
                        ind-=2;
                        list.add(ind,val);
                        res.add(ind);

                    }
                    if(ind-i==1)
                    {
                        int j=i+2;
                        for(int x=0;x<2;x++)
                        {
                            res.add(i);
                            int val=list.remove(j);
                            list.add(i,val);

                        }
                    }
                    else if(ind-i==2)
                    {
                        int j=i+2;
                        for(int x=0;x<1;x++)
                        {
                            res.add(i);
                            int val=list.remove(j);
                            list.add(i,val);

                        }
                    }

                }
//                System.out.println(list);

            }
//            System.out.println(res.size());


                int last=-1;
                for(int i=0;i<n-1;i++)
                {
                    if(list.get(i)>list.get(i+1))
                    {

                        last=i;
                        break;
                    }
                }
                if(last==-1)
                {
                    ans.append(res.size()).append("\n");
                    for (int i : res) {
                        ans.append(i + 1).append(" ");
                    }
                    ans.append("\n");
                }
                else
                {
                    int flag=0;
                    int lastVal=list.get(last);
                    for(int i=last+1;i<list.size();i++)
                    {
                        if(list.get(i)>=lastVal)
                        {
                            lastVal=list.get(i);
                            continue;
                        }
                        if(!set.contains(list.get(i)))
                        {
                            flag=1;
                            break;
                        }
                        else
                        {
                            int j=i;
                            while(j>1)
                            {
                                int val=list.remove(j);
                                j-=2;
                                res.add(j);
                                list.add(j,val);
                                if(j>0)
                                {
                                    if(list.get(j+1)==val || list.get(j-1)==val)
                                    {
                                        break;
                                    }
                                }
                                else
                                {
                                    if(list.get(j+1)==val)
                                    {
                                        break;
                                    }
                                }
                            }


                        }
                    }
                    if(flag==1)
                    {
                        ans.append("-1\n");
                    }
                    else {
                        ans.append(res.size()).append("\n");
                        for (int i: res) {
                            ans.append(i + 1).append(" ");
                        }
                        ans.append("\n");
                    }
                }

        }
        out.print(ans.toString());
        out.flush();

    }
}