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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class MathUtils
{
    static Scanner sc = new Scanner(System.in);
	public static void main (String[] args) throws java.lang.Exception
	{
		int t,n,k,temp,i,j,local;
		int[] arr;
		t= sc.nextInt();
		while(t-->0){
		    n=sc.nextInt();
		    k=sc.nextInt();
		    arr = new int[n];
		    
		    for(i=0;i<n;i++){
		        arr[i]=i+1;
		    }
		    
		   
		    temp= (n-1)/2;
		    if(temp>=k){
		        for(i=2,j=0;i<n&&j<k;i=i+2,j++){
		            local=arr[i];
		            arr[i]=arr[i-1];
		            arr[i-1]=local;
		        }
		        for(i=0;i<n;i++){
		            System.out.print(arr[i]+" ");
		        }
		        System.out.println();
		    }
		    else{
		        System.out.println("-1");
		    }
		    
		}
	}
}