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 ArraryAnsPeaks {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            int k = in.nextInt();
            if (n % 2 == 0 && k > ((n / 2) - 1)) {
                System.out.println(-1);
                continue;
            } else if (n % 2 == 1 && k > n / 2) {
                System.out.println(-1);
                continue;
            }
            int[] ans = new int[n];
            int numberPut = n, pos = 1;
            for (int i = 0; i < k; i++) {
                ans[pos] = numberPut;
                numberPut--;
                pos += 2;
            }

            numberPut = 1;
            for (int i = 0; i < n; i++) {
                if (ans[i] == 0) {
                    ans[i] = numberPut++;
                }
            }
            for (int i : ans) {
                System.out.print(i + " ");
            }
            System.out.println();
        }
    }
}