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.Scanner;
public class HashemZerei {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t-->0){
            int n = in.nextInt();
            int k = in.nextInt();
            int []a= new int [n];
            for(int  i = 0; i < n ; i++){
                a[i]=i+1;
            }
            if(n<=2 && k>0)
                System.out.println("-1");
            else if(n<=2 && k==0)
            {
     		for(int i = 0;i<=n-1; i++)
                {
                    System.out.print(a[i]+" ");
                }
     		         System.out.println("");	
            }
            else if(n==k)
                System.out.println("-1");
            else if(n%2==0){
                if(k<=n/2 -1){
				int c = 0;
				for(int i = 1 ; i < n-1 ; i++){
					if(c==k)
						break;
					if(i%2==1){
                                            int temp = a[i];
					a[i]=a[i+1];
					a[i+1]=temp;
					c++;
                                        }
				}
				for(int i = 0 ; i < n ; i++)
                                {
                                    System.out.print(a[i]+" ");
                                }
                                System.out.println("");
			}
			else
			                 System.out.println("-1");
            }
            else if(n%2==1){
                if(k<=n/2){
				int c = 0;
				for(int i = 1 ; i < n-1 ; i++){
					if(c==k)
						break;
					if(i%2==1){
                                            int temp = a[i];
					a[i]=a[i+1];
					a[i+1]=temp;
					c++;
                                        }
				}
				for(int i = 0 ; i < n ; i++)
                                {
                                    System.out.print(a[i]+" ");
                                }
                                System.out.println("");
			}
			else
			                 System.out.println("-1");
            }
        }
    }
}