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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;


import java.util.*;

import static java.lang.Math.min;
import static java.lang.Math.max;
import static java.lang.Math.abs;

// thanks be to Lord and Mary
public class sol {

    static PrintWriter out = new PrintWriter(System.out);
    static FastScanner in = new FastScanner();



    static void solve () {
        int n = in.nextInt();
        int k = in.nextInt();

        if((n-1)/2<k) {
            out.println(-1);
        } else {
            int[] ans = new int[n];
            ans[0] = 1;
            for(int i = 1;i<2*k;i+=2) {
                ans[i] = i+2;
                ans[i+1] = i+1;
            }

                for (int i = 2 * k + 1; i < n; i++) {
                    ans[i] = i + 1;
                }

            for(int i = 0;i< n;i++ ) {
                out.print(ans[i] + " " );
            }
            out.println();
        }

    }



    //DO NOT FORGET TO DELETE PACKAGE NAME!!!
    //also don't forget to check the value t
    //use long or int as needed







    public static void main(String[] args ) {
        int t = 1;
        t = in.nextInt();
        //double sTime = System.nanoTime();
        for(int i = 0;i< t;i++ ) {
            solve();
            //double eTime = System.nanoTime();
            //out.println((eTime-sTime)/1000000);
        }

        out.close();
    }








    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
// Who am I?