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.ArrayList;
import java.util.List;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution {
    static final FS sc = new FS();  // 封装输入类
    static final PrintWriter pw = new PrintWriter(System.out);
    static List<Integer> res;
    
    public static void main(String[] args) {
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
            }
            solve(n, a);
            if (res == null) {
                pw.println(-1);
                continue;
            }
            pw.println(res.size());
            for (int x : res) {
                pw.print(x + 1 + " ");
            }
            pw.println();
        }

        pw.flush();
    }

    public static void solve(int N, int[] A) {
        res = 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);
                    min++;
                } else {
                    shift(A, min - 2);
                    min -= 2;
                }
            }
        }
        if (A[N - 2] <= A[N - 1]) {
            return;
        }
        if (A[N - 3] == A[N - 1]) {
            shift(A, N - 3);
            return;
        }
        int idx = -1;
        for (int i = 0; i < N - 1; i++) {
            if (A[i] == A[i + 1]) {
                idx = i;
                break;
            }
        }
        if (idx == -1) {
            res = null;
            return;
        }
        for (int i = 0; i < 4; i++) {
            shift(A, idx + i / 2);
        }
        for (int i = idx + 2; i < N - 2; i++) {
            for (int j = 0; j < 2; j++) {
                shift(A, i);
            }
        }
    }

    public static void shift(int[] a, int i) {
        int tmp = a[i + 2];
        a[i + 2] = a[i + 1];
        a[i + 1] = a[i];
        a[i] = tmp;
        res.add(i);
    }


    static class FS {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while(!st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(Exception ignored) {}
            }
            return st.nextToken();
        }
        int[] nextArray(int n) {
            int[] a = new int[n];
            for(int i = 0;i < n;i++) {
                a[i] = nextInt();
            }
            return a;
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}