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:
/*
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Don't let that studying and grades consume you
Just live life young
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That means I'm on top of my game and it don't stop
til my hip don't hop anymore
https://www.a2oj.com/Ladder16.html
*******************************
300IQ as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class F
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int T = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         while(T-->0)
         {
            int N = Integer.parseInt(infile.readLine());
            int[] arr = new int[N];
            st = new StringTokenizer(infile.readLine());
            for(int i=0; i < N; i++)
               arr[i] = Integer.parseInt(st.nextToken());
            int inversions = invcnt(arr);
            if(distinct(arr) && inversions%2 == 1)
               sb.append("-1\n");
            else
            {
               if(inversions%2 == 1)
               {
                  int a = -1; int b = -1;
                  int doubled = -1;
                  matcha:for(int i=0; i < N; i++)
                     for(int j=i+1; j < N; j++)
                        if(arr[i] == arr[j])
                        {
                           a = i;
                           b = j;
                           doubled = arr[i];
                           break matcha;
                        }
                  //permutation
                  ArrayList<Thing> temp = new ArrayList<Thing>();
                  for(int i=0; i < N; i++)
                     temp.add(new Thing(i, arr[i]));
                  Collections.sort(temp);
                  int boof = 0;
                  for(Thing t: temp)
                     arr[t.dex] = boof++;
                  int t = arr[a];
                  arr[a] = arr[b];
                  arr[b] = t;
               }
               else
               {
                  //normal compression
                  ArrayList<Thing> temp = new ArrayList<Thing>();
                  for(int i=0; i < N; i++)
                     temp.add(new Thing(i, arr[i]));
                  Collections.sort(temp);
                  int boof = 0;
                  for(Thing t: temp)
                     arr[t.dex] = boof++;
               }
               //swaps
               ArrayList<Integer> moves = new ArrayList<Integer>();
               for(int curr=0; curr < N; curr++)
               {
                  int loc = -1;
                  for(int i=0; i < N; i++)
                     if(arr[i] == curr)
                     {
                        loc = i;
                        break;
                     }
                  while(loc > curr)
                  {
                     if(loc-1 == curr)
                     {
                        moves.add(curr);  moves.add(curr);
                        shift(arr, curr); shift(arr, curr);
                        loc--;
                     }
                     else
                     {
                        moves.add(loc-2);
                        shift(arr, loc-2);
                        loc -= 2;
                     }
                  }
               }
               sb.append(moves.size()+"\n");
               for(int x: moves)
                  sb.append(x+1).append(" ");
               sb.append("\n");
            }
         }
         System.out.print(sb);
      }
      public static void shift(int[] arr, int dex)
      {
         int a = arr[dex];
         int b = arr[dex+1];
         int c = arr[dex+2];
         arr[dex] = c;
         arr[dex+1] = a;
         arr[dex+2] = b;
      }
      public static int invcnt(int[] arr)
      {
         int res = 0;
         for(int a=0; a < arr.length; a++)
            for(int b=a+1; b < arr.length; b++)
               if(arr[a] > arr[b])
                  res++;
         return res;
      }
      public static boolean distinct(int[] arr)
      {
         HashSet<Integer> set = new HashSet<Integer>();
         for(int x: arr)
            if(!set.add(x))
               return false;
         return true;
      }
   }
   class Thing implements Comparable<Thing>
   {
      public int val;
      public int dex;
      
      public Thing(int a, int b)
      {
         dex = a;
         val = b;
      }
      public int compareTo(Thing oth)
      {
         if(val == oth.val)
            return dex-oth.dex;
         return val-oth.val;
      }
   }