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 Solution{
  static Scanner sc = new Scanner(System.in);
    static void output(){
        int n = sc.nextInt();
        int k = sc.nextInt();
        if(n<=k*2){
            System.out.println(-1);
            return;
        }
        int i=1,j=n;
        for(int x=1;x<=k*2+1;x++){
            if(x%2 != 0){
            System.out.print(i+" ");
            i++;
            }
            else{
                System.out.print(j+" ");
                j--; 
            }
        }
        for(int x=i;x<=j;x++)
            System.out.print(x+" ");
        System.out.println();
    }
    public static void main(String[] args) {
        
        int t = sc.nextInt();
        for(int i=1;i<=t;i++){
          output();
        }
        }
}