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.*;
import java.lang.*;
import java.math.BigInteger;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class B
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		StringBuilder sb = new StringBuilder();
		int t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			int k = sc.nextInt();
			int res = -1;
			int peak = 0;
			int arr[] = new int[n];
			for(int i=1;i<=n;i++){
				arr[i-1] = i;
			}
			int ind = 1;
			while(ind<n-1 && peak!=k) {
				int temp = arr[ind];
				arr[ind] = arr[ind+1];
				arr[ind+1] = temp;
				ind+=2;
				peak++;
			}
			if(peak==k) {
				for(int i=0;i<n;i++){
					sb.append(arr[i]+" ");
				}
			}
			else {
				sb.append("-1");
			}
			sb.append("\n");
		}
		System.out.print(sb.toString());
	}
}