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 final class q4 {
    public static void main(String[] Args){
        Scanner s= new Scanner(System.in);
        int t = s.nextInt();
        s.nextLine();
        while(t>0){
            int n = s.nextInt();
            int k = s.nextInt();
            s.nextLine();
            if(n%2 == 0  && (n/2)-1 < k){
                System.out.println(-1);
            }

            else if(n%2!=0 && n/2 < k){
                System.out.println(-1);
            }
            else if(k<n){
                System.out.print(1);
                System.out.print(" ");

                int count =0;
                for(int i=1;i<n-1;i+=2){
                    if(count<k){
                    System.out.print(i+2);
                    System.out.print(" ");
                    System.out.print(i+1);
                    System.out.print(" ");
                    count++;
                    }
                    else{
                        System.out.print(i+1);
                        System.out.print(" ");
                        System.out.print(i+2);
                        System.out.print(" ");
                    }
                    
                    
                }
                if(n%2==0){
                    System.out.print(n);
                }
                System.out.println("");
            }
            else{
                System.out.println(-1);
            }
            t--;
        }
    }
}