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:
/*
 ID: tommatt1
 LANG: JAVA
 TASK: 
*/
import java.util.*;
import java.io.*;
public class cf1374f{

	public static void main(String[] args)throws IOException {
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer(bf.readLine());
		int tt=Integer.parseInt(st.nextToken());
		while(tt-->0) {
			st=new StringTokenizer(bf.readLine());
			int n=Integer.parseInt(st.nextToken());
			int[] a=new int[n];
			st=new StringTokenizer(bf.readLine());
			for(int i=0;i<n;i++) {
				a[i]=Integer.parseInt(st.nextToken());
			}
			ArrayList<Integer> ans=new ArrayList<Integer>();
			for(int t=0;t<n;t++) {
				for(int i=0;i<n-2;i++) {
					if(a[i]>a[i+1]) {
						int tmp=a[i];
						a[i]=a[i+1];
						a[i+1]=a[i+2];
						a[i+2]=tmp;
					    ans.add(i+1);ans.add(i+1);
					}
					else if(a[i+1]>a[i+2]) {
						int tmp=a[i+2];
						a[i+2]=a[i+1];
						a[i+1]=a[i];
						a[i]=tmp;
						ans.add(i+1);
					}
				}
			}
			boolean pass=true;
			for(int i=0;i<n-1;i++) {
				if(a[i+1]<a[i]) {
					out.println(-1);
					pass=false;
				}
			}
			if(pass) {
			out.println(ans.size());
			for(int i=0;i<ans.size();i++) {
				out.print(ans.get(i)+" ");
			}
			out.println();
			}
		}
		out.close();
	}

}