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.*;
import java.io.*;
public class Main
{
  public static void main(String[] args) throws IOException
  {
    Scanner read = new Scanner(System.in);
    
    int t = read.nextInt();
    for(int x = 1; x<=t; x++)
    {
      int n = read.nextInt();
      int k = read.nextInt();
      
      if(n == k || (n % 2 == 0 && k >= n / 2) || (n % 2 == 1 && k >= n / 2 + 1))
      {
        System.out.println(-1);
      }
      else
      {
        int max = n - k + 1;
        boolean [] mark = new boolean[n+1];
        System.out.print(1+" ");
        for(int i = 2; i<=n; i++)
        {
          if(k == 0)
          {
            if(!mark[i])
            {
              System.out.print(i+" ");
            }
          }
          else
          {
            mark[max] = true;
            mark[i] = true;
            System.out.print(max+" ");
            System.out.print(i+" ");
            max++;
            k--;
          }
        }
        System.out.println();
      }
    }
  }
}