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.io.*;
import java.util.*;


public class ArrayandPeaks {

    public static void main(String[] args) throws IOException {
       Scanner sc = new Scanner(System.in);
       int t_c = sc.nextInt();
       while(t_c-- > 0){
           int n = sc.nextInt();
           int k = sc.nextInt();
           int res[] = new int[n];
           for(int i = 0; i < n ; i++){
               res[i] = i + 1;
           }
           if(k * 2 >= n){
               System.out.println(-1);
               continue;
           }
           for(int i = 0; i < k; i++){
               int a = i * 2 + 1;
               int b = a + 1;
               int temp = res[a];
               res[a] = res[b];
               res[b] = temp;
           }

           for(int i : res){
               System.out.print(i + " ");
           }
           System.out.println();
           }
       }
}