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.*;

public class f {
    public static int[] arr;
    public static ArrayList<Integer> ans;
    public static void main(String[] Args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-->0) {
            int n = sc.nextInt();
            arr = new int[n];
            int[] perfect = new int[n];
            int invs = 0;
            boolean hasDupes = false;

            for (int i = 0; i < n; i++) {
                perfect[i] = arr[i] = sc.nextInt();
                for (int j = 0; j < i; j++)
                    if (arr[i] < arr[j])
                        invs++;
            }
            Arrays.sort(perfect);
            for (int i = 0; i < n - 1; i++)
                if (perfect[i] == perfect[i + 1])
                    hasDupes = true;


            if (!hasDupes && invs % 2 == 1) {
                System.out.println(-1);
                continue;
            }
            ans = new ArrayList<Integer>();
            for (int i = 1; i <= n; i++) {
                int j = i - 1;
                while (arr[j] != perfect[i - 1]) {
                    j++;
                }
                while (j != i - 1) {
                    if (j == i && i != n - 1) {
                        press(i);
                        press(i);
                        j--;
                    } else if (n != i + 1) {
                        press(j - 1);
                        j-=2;
                    } else {
                        j = n - 1;
                        while (arr[j] != perfect[j]) {
                            press(j - 1);
                            j--;
                        }
                        j = i - 1;
                    }
                }
            }
            System.out.println(ans.size());
            for (Integer x : ans)
                System.out.print(x + " ");
            System.out.println();
        }
    }

    public static void press(int i) {
        ans.add(i);
        int tmp  = arr[i - 1];
        arr[i-1] = arr[i + 1];
        arr[i+1] = arr[i];
        arr[i] = tmp;
    }
}