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.Scanner;

public class round714 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int T = in.nextInt();
        while (T-- > 0) {
            int n = in.nextInt(), k = in.nextInt();
            int[] a = new int[n+1];

            if (k > (n-1)/2) {
                System.out.println(-1);
                continue;
            }

            int num = n;
            for (int i = 2; i < a.length && k > 0; i += 2, k--) a[i] = num--;

            for (int i = 1; i < a.length; i++) {
                if (a[i] == 0) a[i] = num--;
            }

            StringBuilder builder = new StringBuilder();
            for (int i = 1; i < a.length; i++) builder.append(a[i]).append(" ");

            System.out.println(builder);
        }
    }
}