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.util.*;
import java.util.stream.Collectors;

public final class Constructive {

    private static final FastReader fr = new FastReader();

    public static void main(String[] args) {
        int t = fr.nextInt();
        while (t-- > 0) {
            int[] input = readArray();
            int[] steps = new CyclicShiftsSorting(input).solve();

            if (steps == null) System.out.println(-1);
            else {
                System.out.println(steps.length);
                for (int step : steps) {
                    System.out.print((step + 1) + " ");
                }
                System.out.println();
            }
        }
    }

    private static final class CyclicShiftsSorting {
        private final int[] input;
        private final List<Integer> current;

        public CyclicShiftsSorting(final int[] input) {
            this.input = input;
            current = Arrays.stream(input).boxed().collect(Collectors.toList());
        }

        public int[] solve() {
            Queue<Integer> steps = new ArrayDeque<>();

            while (current.size() > 2) {
                int i = current.indexOf(Collections.min(current));
                while (i > 0) {
                    if (i - 2 >= 0) {
                        cycle(i - 2);
                        steps.add(actualIndex(i - 2));
                        i -= 2;
                    } else {
                        cycle(0);
                        steps.add(actualIndex(0));
                        i += 1;
                    }
                }
                current.remove(0);
            }

            if (isSorted()) return steps.stream().mapToInt((i) -> i).toArray();
            else {
                current.addAll(0, Arrays.stream(input).sorted().limit(input.length - 2).boxed().collect(Collectors.toList()));
                for (int i = current.size() - 1; i >= 2; i--) {
                    cycle(i - 2);
                    steps.add(i - 2);
                    if (isSorted()) break;
                }
                if (isSorted()) return steps.stream().mapToInt((i) -> i).toArray();
                else return null;
            }
        }

        private int actualIndex(int i) {
            return input.length - current.size() + i;
        }

        private boolean isSorted() {
            int prev = Integer.MIN_VALUE;
            for (int value : current) {
                if (value < prev) return false;
                prev = value;
            }
            return true;
        }

        private void cycle(int i) {
            Collections.swap(current, i + 1, i + 2);
            Collections.swap(current, i, i + 1);
        }

    }

    private static int[] readArray() {
        int[] arr = new int[fr.nextInt()];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = fr.nextInt();
        }
        return arr;
    }

    private static final class FastReader {
        private final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st;

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

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

}