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.lang.String;
import java.math.BigInteger;
import java.util.List;
import java.util.ArrayList;
import java.util.Scanner;
import java.lang.Math;
import java.util.Arrays;


public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    
    int nSolutions = Integer.parseInt(scanner.nextLine());

    // n, k
    for (int i = 0; i < nSolutions; i++) {
      int[] params = parseInputString(scanner.nextLine());

      List<String> asStrings = new ArrayList<String>(nSolutions);
      solve(params[0], params[1]).forEach((integer) -> {
        asStrings.add(Integer.toString(integer.intValue()));
      });

      System.out.println(String.join(" ", asStrings));
    }
  }

  /**
   * Construct an array of length n with k peaks
   */
  private static List<Integer> solve(int n, int k) {
    if (k > n/2) return Arrays.asList(-1);
    List<Integer> solution = new ArrayList<Integer>(n); 
    
    for (int i = 1; i <= n; i++) {
      solution.add(i);
    }   

    // 1 2 3 4 5
    for (int i = 0, j = 1; i < k; i++) {
      if (j + 1 >= solution.size()) return Arrays.asList(-1) ;
      
      swap(solution, j, j + 1);
      j += 2;
    }

    return solution;
  }

  private static void swap(List<Integer> arr, int i, int j) {
    Integer tmp = arr.get(i);
    arr.set(i, arr.get(j));
    arr.set(j, tmp);
  }

  private static int[] parseInputString(String input)  {
    String[] tokens = input.split(" ");
    int[] result = new int[tokens.length];
    int i = 0;
    for (String token : tokens) {
      result[i] = Integer.parseInt(token);
      ++i;
    }
    return result;
  }

}