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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 * @author Sergei Britvin <ljql@yandex-team.ru>
 * Created at 15.04.2021
 */
public class First {
    public static void main(String[] args) throws IOException {
        BufferedReader b = new BufferedReader(new InputStreamReader(System.in));

        int t = Integer.parseInt(b.readLine());
//        int t = 1;
        for (int i = 0; i < t; i ++) {
            String[] s = b.readLine().split(" ");
//            String[] s = "5 2".split(" ");
            int n = Integer.parseInt(s[0]);
            int k = Integer.parseInt(s[1]);

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

            int[] array = getStartArray(n);

            int j = 0;
            int ind = 1;
            boolean error = false;
            while (j < k) {
                if (ind >= n-1) {
                    error = true;
                    break;
                }
                array[ind] = array[ind] ^ array[ind + 1];
                array[ind + 1] = array[ind + 1] ^ array[ind];
                array[ind] = array[ind] ^ array[ind + 1];

                j+=1;
                ind += 2;
            }
            if (error) {
                System.out.println(-1);
                continue;
            }
            System.out.println(outArray(array));
        }
    }

    public static int[] getStartArray(int n) {
        int[] result = new int[n];
        for (int i = 0; i < n; i ++) {
            result[i] = i+1;
        }
        return result;
    }

    public static String outArray(int[] array) {
        StringBuilder result = new StringBuilder();
        for (int i = 0; i < array.length - 1; i++) {
            result.append(array[i] + " ");
        }
        result.append(array[array.length - 1]);
        return result.toString();
    }
}