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.*;
public class Main
{
	public static void main(String[] args) {
		Scanner enter = new Scanner(System.in);
		int t = enter.nextInt();
		while(t-- != 0){
		    int n = enter.nextInt();
		    int k = enter.nextInt();
		    if(k==0){
		        for(int i=1;i<=n;i++){
		            System.out.print(i+" ");
		        }
		    }else if(n%2 == 1){
		        if(k>(n/2)){
		            System.out.print("-1");
		        }else{
		            int arr[] = new int[n];
		            for(int l=0;l<n;l++){
		                arr[l] = l+1;
		            }int i=1,j=2;
		            while(k-- != 0 && j<n){
		                int temp = arr[i];
		                arr[i] = arr[j];
		                arr[j] = temp;
		                i+=2;
		                j+=2;
		            }
		            for(int l=0;l<n;l++){
		                System.out.print(arr[l]+ " ");
		            }
		        }
		    }else{
		        if(k>((n/2)-1)){
		            System.out.print("-1");
		        }else{
		            int arr[] = new int[n];
		            for(int l=0;l<n;l++){
		                arr[l] = l+1;
		            }int i=1,j=2;
		            while(k-- != 0 && j<n){
		                int temp = arr[i];
		                arr[i] = arr[j];
		                arr[j] = temp;
		                i+=2;
		                j+=2;
		            }
		            for(int l=0;l<n;l++){
		                System.out.print(arr[l] + " ");
		            }
		        }
		    }
		    System.out.println();
		}
	}
}