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.*;
import java.lang.*;
import java.math.BigInteger;
import java.util.*;
public class Main{
	static Scanner scanner=new Scanner(System.in);
	static BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
	public static void main(String[] args) throws NumberFormatException, IOException {
		int q=scanner.nextInt();
		l:while(q-->0) {
			int n=scanner.nextInt();
			int k=scanner.nextInt();
			if(k>(n-1)/2) {
				System.out.println(-1);
				continue;
			}else {
				int a[]=new int [n];
				for(int i=0;i<n;i++)a[i]=i+1;
				for(int i=1;i<n&&k>0;i+=2) {
					{int temp=a[i];a[i]=a[i+1];a[i+1]=temp;}
					k--;
				}
				StringBuilder sb=new StringBuilder();
				for(int i=0;i<n;i++)sb.append(a[i]+" ");
				System.out.println(sb);
			}
		}
	}
}