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 Codeforces2 {

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

                for(int i=0;i<n;i++) System.out.print(arr[i]+" ");
                System.out.println();
            }

        }
    }
}