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.*;

public class DadaBC{
    public static void main(String ...args){
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        while(T--!=0){
            int n=sc.nextInt();
            int k=sc.nextInt();
            if(k==0){
                for(int i=n;i>=1;i--){
                    System.out.print(i+" ");
                }
                System.out.print("\n");
            }else{
                // max peaks can be n/2
                int maxPeaks = n%2==0?n/2-1:n/2;
                if(k>maxPeaks){
                    System.out.println("-1");
                    continue;
                }
                // print pattern
                int i=1,j=n;
                int i_lim=n%2==0?n/2:n/2+1;
                int j_lim=n%2==0?n/2+1:n/2+2;
                //System.out.println(i_lim+" jlim="+j_lim);
                // print maxPeaks if reqd
                if(k==maxPeaks){
                     while(i<=i_lim && j>=j_lim){
                        System.out.print(i+" "+j+" ");
                        
                        i++;
                        j--;
                    
                    }
                    if(n%2!=0)
                    System.out.print(i+" ");
                    if(j==j_lim)
                    System.out.print(j+" ");
                    System.out.println();
                }else{
                    // if maxPeaks not reqd
                    // print maxpeaks then print in desc
                    int peaks=0;
                    while(peaks!=k){
                        System.out.print(i+" "+j+" ");
                        i++;
                        j--;
                        peaks++;
                    }
                    for(int ss=j;ss>=i;ss--){
                        System.out.print(ss+" ");
                    }
                    System.out.println();
                    
                }
               
            }
        }
    }
}