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:
/* package whatever; // don't place package name! */

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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
int t=Integer.parseInt(br.readLine());

    	for(int j=0; j<t; j++)
    	{    int n,k;
    String str=br.readLine();
    StringTokenizer st=new StringTokenizer(str, " ");
    		n=Integer.parseInt(st.nextToken());
    		k=Integer.parseInt(st.nextToken());
    		int max=(n-1)/2;
    		if(k>max)
    		{
    			System.out.println("-1");
    			continue;
    		}
    		 int s=1; int e=n; 
    		 for(int i=1; i<=k; i++)
    		 {
    		 		System.out.print((s++)+" "+(e--)+" ");
    		 	
    		 }
    		 for(int i=s; i<=e; i++)
    		 {
    		 	System.out.print(i+" ");
    		 }
    		 System.out.println();
    	}
	}
}