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.util.*;
import java.util.Map.Entry;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class GFG
{
	
	


	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc=new Scanner(System.in);
	    int k=sc.nextInt();
	    int arr[];
	    while(k>0){
	        int peak=0;
	        int n=sc.nextInt();
	        int a=sc.nextInt();
	        arr=new int[n];
	        for(int i=0;i<n;i++){
	            arr[i]=i+1;
	        }
	        if(a!=0){
	            for(int j=1;j<n-1;j+=2){
	                int temp=arr[j];
	                arr[j]=arr[j+1];
	                arr[j+1]=temp;
	                peak++;
	                if(peak==a){
	                    break;
	                }
	            }
	            if(peak!=a){
	                System.out.println(-1);
	            }else{
	                for(int i=0;i<n;i++){
	                    System.out.print(arr[i]+" ");
	                }
	            }
	        }else {
	        	for(int i=0;i<n;i++){
                    System.out.print(arr[i]+" ");
                }
	        }
	        
	        k--;
	    }
	}
}