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 Main {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        l:for(int t=sc.nextInt();t-->0;) {
            int n=sc.nextInt(),k=sc.nextInt(),a[]=new int[n],x=1;
            boolean used[]=new boolean[n+1];
            if(k>=(n+1)/2) {System.out.println(-1);continue l;}
            for(int i=1;i<a.length&&k>0;i+=2,k--) {
                a[i]=n;
                used[n--]=true;
            }
            for(int i=0;i<a.length;i++) {
                if(a[i]==0) {
                    while(used[x]) x++;
                    a[i]=x;
                    used[x]=true;
                }
            }
            for(int i:a) System.out.print(i+" ");
            System.out.println();
        }
    }
}