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.*;

public class Problem_F {
	public static void shift(int[] A, int idx) {
		int tmp = A[idx + 2];
		A[idx + 2] = A[idx + 1];
		A[idx + 1] = A[idx];
		A[idx] = tmp;
	}

	public static List<Integer> solve(int N, int[] A) {
		List<Integer> path = new ArrayList<>();
		for (int i = 0; i < N - 2; i++) {
			int min = i;
			for (int j = i; j < N; j++) {
				if (A[min] > A[j]) {
					min = j;
				}
			}
			while (min > i) {
				if (min - i == 1) {
					shift(A, i);
					path.add(i);
					min++;
				} else {
					shift(A, min - 2);
					path.add(min - 2);
					min -= 2;
				}
			}
		}
		if (A[N - 2] <= A[N - 1]) {
			return path;
		}
		if (A[N - 3] == A[N - 1]) {
			shift(A, N - 3);
			path.add(N - 3);
			return path;
		}
		int idx = -1;
		for (int i = 0; i < N - 1; i++) {
			if (A[i] == A[i + 1]) {
				idx = i;
				break;
			}
		}
		if (idx == -1) {
			return null;
		}
		for (int i = 0; i < 4; i++) {
			shift(A, idx + i / 2);
			path.add(idx + i / 2);
		}
		for (int i = idx + 2; i < N - 2; i++) {
			for (int j = 0; j < 2; j++) {
				shift(A, i);
				path.add(i);
			}
		}
		return path;
	}

	public static void main(String[] args) {
		InputReader in = new InputReader();
		StringBuilder out = new StringBuilder();

		int T = in.nextInt();
		while (T-- > 0) {
			int N = in.nextInt();
			int[] A = new int[N];
			for (int i = 0; i < N; i++) {
				A[i] = in.nextInt();
			}
			List<Integer> path = solve(N, A);
			if (path == null) {
				out.append("-1\n");
				continue;
			}
			out.append(path.size()).append('\n');
			for (int x : path) {
				out.append(x + 1).append(' ');
			}
			if (path.isEmpty()) {
				out.append('\n');
			} else {
				out.setCharAt(out.length() - 1, '\n');
			}
		}

		System.out.print(out);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer st;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

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

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

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