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

        for (int i = 0; i < n; i++) {
            String[] dataIn = scanner.nextLine().split(" ");
            int j = Integer.parseInt(dataIn[0]);
            int k = Integer.parseInt(dataIn[1]);

            if (k > ((j+1)/2)-1) {
                System.out.println(-1);
            } else {
                for (int l = 1; l <= k; l++) {
                    System.out.print(l + " ");
                    System.out.print((j - l + 1) + " ");
                }
                for (int l = k*2+1; l <= j; l++) {
                    System.out.print((l - k) + " ");
                }
            }
            System.out.println();
        }
    }
}