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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t;
    cin>>t;

    while(t--)
    {
        int n,k;
        cin>>n>>k;

        if(k==0)
        {
            for(int i=1;i<=n;i++)
            cout<<i<<" ";

            cout<<endl;
            continue;
        }

        else if(n%2==0 && k>=(n/2))
        {
            cout<<-1<<endl;
            continue;
        }

        else if(n%2!=0 && k>=(n/2)+1)
        {
            cout<<-1<<endl;
            continue;
        }

        else
        {   
            int arr[n+1];
            arr[0]=0,arr[1]=1,arr[n]=n;
            int count_peak=0,count_no=0;
            bool flag=true;
            int temp=3;
            for(int i=2;i<=n-1;i+=2)
            {   
                if(count_peak<k)
                {
                    arr[i]=temp;
                    temp+=2;
                    count_peak++;
                    count_no++;
                }

                else
                {
                    flag=false;
                    break;
                }

                /*if(flag==true)
                break;
                
                if(count==k)
                flag=false;
*/
            }
            
            if(flag==true)
            {
                temp=2;
                for(int i=3;i<=n;i+=2)
                {   
                    arr[i]=temp;
                    temp+=2;
                }
            }

            else if(flag==false)
            {
               int temp1=0,temp2=0;
               temp=2;
               for(int i=3;i<=n;i+=2)
                {   
                    if(temp1<k)
                    {
                        arr[i]=temp;
                        temp+=2;
                        temp1++;
                        temp2=temp;
                    }
                }

                temp2+=2;

                for(int i=temp;i<n+1;i++)
                {
                    arr[i]=i;
                }



            }

            for(int i=1;i<n+1;i++)
            cout<<arr[i]<<" ";

            cout<<endl;



        }




    }


    return 0;
}