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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		int T = sc.nextInt();
		tt:for(int t =0; t<T; t++){
		    int N = sc.nextInt(), K = sc.nextInt();
		    if(K > (N - 1) / 2)out.println(-1);
		    else{
		        int k = 3;
		        out.print(1 + " ");
		        int cnt = 0;
		        if(K != 0){
		            for(int i = 2; i<=N; i+=2){
		            out.print(k + " ");
		            cnt++;
		            out.print(i + " ");
		            if(cnt == K)break;
		            k+=2;
		        }
		        }
		        else{
		            for(int i = 2; i<=N; i++)out.print(i + " ");
		            out.println(); continue tt;
		        }
		        for(int i = k + 1; i<=N; i++)out.print(i + " ");
		        out.println();
		    }
		}
		out.flush();
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try { 
                                        st=new StringTokenizer(br.readLine());				               
                                } catch (IOException e) {}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}