Problem: A sequence of n integers is called a permutation if it contains all integers from 1 to n exactly once.

Given two integers n and k, construct a permutation a of numbers from 1 to n which has exactly k peaks. An index i of an array a of size n is said to be a peak if 1 < i < n and a_i \gt a_{i-1} and a_i \gt a_{i+1}. If such permutation is not possible, then print -1.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases.

Then t lines follow, each containing two space-separated integers n (1 ≤ n ≤ 100) and k (0 ≤ k ≤ n) — the length of an array and the required number of peaks.

Output

Output t lines. For each test case, if there is no permutation with given length and number of peaks, then print -1. Otherwise print a line containing n space-separated integers which forms a permutation of numbers from 1 to n and contains exactly k peaks. 

If there are multiple answers, print any.

Example

Input


5
1 0
5 2
6 6
2 1
6 1


Output


1 
2 4 1 5 3 
-1
-1
1 3 6 5 4 2

Note

In the second test case of the example, we have array a = [2,4,1,5,3]. Here, indices i=2 and i=4 are the peaks of the array. This is because (a_{2} \gt a_{1} , a_{2} \gt a_{3}) and (a_{4} \gt a_{3}, a_{4} \gt a_{5}). 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

@SuppressWarnings("DuplicatedCode")
public class Main {
    static PrintWriter pw;
    static _Scanner sc;

    public static void main(String[] args) throws Exception {
        sc = new _Scanner(System.in);
        pw = new PrintWriter(System.out);
        //long startTime = System.currentTimeMillis();

        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
        pw.flush();
        //System.out.println("time: " + (System.currentTimeMillis() - startTime));
    }

    private static void solve() throws Exception {
        int n = sc.nextInt();
        int k = sc.nextInt();

        if (k > (n - 1) / 2) {
            pw.println(-1);
            return;
        }

        pw.print(1);
        pw.print(" ");

        for (int i = 0; i < k; ++i) {
            pw.print((i + 1) * 2 + 1);
            pw.print(" ");
            pw.print((i + 1) * 2);
            pw.print(" ");
        }

        for (int i = k * 2 + 2; i <= n; ++i) {
            pw.print(i + " ");
        }
        pw.println();
    }

    static class Shuffle {
        static void run(int[] in) {
            for (int i = 0; i < in.length; i++) {
                int idx = (int) (Math.random() * in.length);
                int tmp = in[i];
                in[i] = in[idx];
                in[idx] = tmp;
            }
        }

        static void run(long[] in) {
            for (int i = 0; i < in.length; i++) {
                int idx = (int) (Math.random() * in.length);
                long tmp = in[i];
                in[i] = in[idx];
                in[idx] = tmp;
            }
        }

        static <T> void run(List<T> in) {
            for (int i = 0; i < in.size(); i++) {
                int idx = (int) (Math.random() * in.size());
                T tmp = in.get(i);
                in.set(i, in.get(idx));
                in.set(idx, tmp);
            }
        }
    }

    static class _Scanner {
        StringTokenizer st;
        BufferedReader br;

        _Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        _Scanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        String nextToken() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        int[] intArr(int n) throws IOException {
            int[] in = new int[n];
            for (int i = 0; i < n; i++) in[i] = nextInt();
            return in;
        }

        long[] longArr(int n) throws IOException {
            long[] in = new long[n];
            for (int i = 0; i < n; i++) in[i] = nextLong();
            return in;
        }

        int[] intArrSorted(int n) throws IOException {
            int[] in = new int[n];
            for (int i = 0; i < n; i++) in[i] = nextInt();
            Shuffle.run(in);
            Arrays.sort(in);
            return in;
        }

        long[] longArrSorted(int n) throws IOException {
            long[] in = new long[n];
            for (int i = 0; i < n; i++) in[i] = nextLong();
            Shuffle.run(in);
            Arrays.sort(in);
            return in;
        }

        Integer[] IntegerArr(int n) throws IOException {
            Integer[] in = new Integer[n];
            for (int i = 0; i < n; i++) in[i] = nextInt();
            return in;
        }

        Long[] LongArr(int n) throws IOException {
            Long[] in = new Long[n];
            for (int i = 0; i < n; i++) in[i] = nextLong();
            return in;
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(nextToken());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(nextToken());
        }

        char nextChar() throws IOException {
            return nextToken().charAt(0);
        }

        long nextLong() throws IOException {
            return Long.parseLong(nextToken());
        }

        boolean ready() throws IOException {
            return br.ready();
        }
    }
}