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.*;

public class SuperClass {

    static class pair{

        int start;
        int end;

        public pair(int start,int end){
            this.start = start;
            this.end = end;
        }
    }

    public static void main(String args[]) throws IOException{


        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

            int t = Integer.parseInt(br.readLine());

            while(t-->0){


                StringTokenizer st = new StringTokenizer(br.readLine());

                    int n = Integer.parseInt(st.nextToken());
                    int k  = Integer.parseInt(st.nextToken());

                    solve(n,k);

            }

    }

    static void solve(int  n , int k){

        if(n<=2 && k>0){
            System.out.println(-1);
            return;
        }

        else if(k>((n-1)/2)){
            System.out.println(-1);
            return;
        }
        else{
            if(k==0){
                for(int i = 1; i<=n; i++){
                    System.out.print(i+" ");
                }
                System.out.println();
            }
            else{
                int a[] = new int[n];
                Arrays.fill(a,-1);
                int ind = 1;

                for(int i=(n-k+1); i<=n; i++){
                    a[ind] = i;
                    ind+=2;
                }

                int val = 1;
                    for(int i =0; i<n; i++){
                        if(a[i]==-1){
                            a[i] = val;
                            val++;
                        }
                    }

                        for(int e : a){
                            System.out.print(e+" ");
                        }
                System.out.println();
            }
        }
    }

    static boolean isPalindrome(String s){

        StringBuffer sb = new StringBuffer();
        sb.append(s);

            if(s.equals(sb.reverse().toString())){
                return true;
            }
            else{
                return false;
            }
    }

    static boolean subsetsum(int a[] , int n , int sum){

        boolean t[][] = new boolean[n+1][sum+1];

            for(int i =0; i<n+1; i++){
                t[i][0] = true;
            }
            for(int i =1; i<sum+1; i++){
                t[0][i] = false;
            }

                for(int i = 1; i<n+1; i++){
                    for(int j = 1; j<sum+1; j++){

                        if(a[i-1]<=j){
                           t[i][j] = t[i-1][j-a[i-1]] || t[i-1][j];
                        }
                        else{
                            t[i][j] = t[i-1][j];
                        }
                    }
                }

                return t[n][sum];
    }

    static void ruffleSort(int a[]){

        int n = a.length;

        Random r = new Random();

             for(int i = 0; i<n; i++){

                 int oi = r.nextInt(n);
                 int temp = a[oi];
                 a[oi] = a[i];
                 a[i] = temp;
             }

             Arrays.sort(a);
    }

    static void ruffleSort(long a[]){

        int n = a.length;

        Random r = new Random();

            for(int i = 0; i<n; i++){
                int oi = r.nextInt(n);

                    long temp = a[oi];
                    a[oi] = a[i];
                    a[i] = temp;
            }

            Arrays.sort(a);
    }
}