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.util.*;
import java.io.*;
public class R653F{
   public static void main(String[] main) throws Exception{
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      StringTokenizer st = new StringTokenizer(br.readLine());
      PrintWriter out = new PrintWriter(System.out);
      int t = Integer.parseInt(st.nextToken());
      for(int trial = 1; trial <= t; trial++){
         st = new StringTokenizer(br.readLine());
         int n = Integer.parseInt(st.nextToken());
         int[] a = new int[n];
         //int[] index = new int[n];
         st = new StringTokenizer(br.readLine());
         int inv = 0;
         int maxdup = -1;
         HashSet<Integer> used = new HashSet<Integer>();
         for(int i = 0; i < n; i++) {
        	 a[i] = Integer.parseInt(st.nextToken());
        	 if(used.contains(a[i]))
        		 maxdup = Math.max(maxdup,a[i]);
        	 used.add(a[i]);
        	 //index[a[i]] = i;
        	 /*for(int j = 0; j < i; j++)
        		 if(a[j] > a[i])
        			 inv++;*/
         }
         if(inv%2 == 1)
        	 out.println(-1);
         else {
        	 int dupindex = -1;
        	 ArrayList<Integer> moves = new ArrayList<Integer>();
        	 for(int i = 0; i < n-2; i++) {
        		 int min = Integer.MAX_VALUE;
        		 int index = -1;
        		 for(int j = i; j < n; j++) {
        			 if(a[j] < min) {
        				 index = j;
        				 min = a[j];
        			 }
        		 }
        		 while(index != i) {
        			 if(index == i+1) {
        				 int temp = a[i+2];
        				 a[i+2] = a[i+1];
        				 a[i+1] = a[i];
        				 a[i] = temp;
        				 moves.add(i);
        				 index++;
        			 }
        			 else {
        				 a[index] = a[index-1];
        				 a[index-1] = a[index-2];
        				 a[index-2] = min;
        				 moves.add(index-2);
        				 index -= 2;
        			 }
        		 }
        		 if(min == maxdup)
        			 dupindex = index;
        	 }
        	 if(a[n-2] <= a[n-1]) {
	        	 StringJoiner sj = new StringJoiner(" ");
	        	 for(int i = 0; i < moves.size(); i++) {
	        		 sj.add(Integer.toString(moves.get(i)+1));
	        	 }
	        	 out.println(moves.size());
	        	 out.println(sj);
        	 }
        	 else if(n >= 3 && dupindex == n-3 && a[n-1] == a[n-3]) {
        		 StringJoiner sj = new StringJoiner(" ");
	        	 for(int i = 0; i < moves.size(); i++) {
	        		 sj.add(Integer.toString(moves.get(i)+1));
	        	 }
	        	 out.println(moves.size()+1);
	        	 sj.add(Integer.toString(n-2));
	        	 out.println(sj);
        	 }
        	 else if(dupindex != -1) {
        		 dupindex--;
				 a[dupindex+1] = a[dupindex+2];
				 a[dupindex+2] = a[dupindex];
				 moves.add(dupindex);
				 moves.add(dupindex);
				 for(int i = dupindex+1; i < n-2; i++) {
	        		 int min = Integer.MAX_VALUE;
	        		 int index = -1;
	        		 for(int j = i; j < n; j++) {
	        			 if(a[j] < min) {
	        				 index = j;
	        				 min = a[j];
	        			 }
	        		 }
	        		 if(min == maxdup)
	        			 dupindex = index;
	        		 while(index != i) {
	        			 if(index == i+1) {
	        				 int temp = a[i+2];
	        				 a[i+2] = a[i+1];
	        				 a[i+1] = a[i];
	        				 a[i] = temp;
	        				 moves.add(i);
	        				 index++;
	        			 }
	        			 else {
	        				 a[index] = a[index-1];
	        				 a[index-1] = a[index-2];
	        				 a[index-2] = min;
	        				 moves.add(index-2);
	        				 index -= 2;
	        			 }
	        		 }
	        	 }
				 StringJoiner sj = new StringJoiner(" ");
	        	 for(int i = 0; i < moves.size(); i++) {
	        		 sj.add(Integer.toString(moves.get(i)+1));
	        	 }
	        	 out.println(moves.size());
	        	 out.println(sj);
        	 }
        	 else
        		 out.println(-1);
         }
      }
      out.close();
   }
}