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:
// amit
#include<bits/stdc++.h>
#define fast ios_base::sync_with_stdio(0);cin.tie(NULL); cout.tie(NULL);
#define ll long long int
using namespace std;

#define rep(i,n) for(int i=0;i<n;i++)
#define pi pair<ll,ll>
#define pb push_back


int main()

{
   fast;
   int t;cin>>t;
   while(t--)
   {

       int n,k;
       cin>>n>>k;
       int pos=(n-1)/2;
       if(pos<k)
       {

           cout<<"-1\n";
           continue;
       }
       int todo=k*2+1;
       int arr[n+1];int j=1;
       for(int i=1;i<=n;i++)
        arr[i]=i;
       for(int i=1;i<=(todo);i++)
       {
           if((i&1)==1)
           {
               arr[i]=j;
               j++;
           }
       }
       for(int i=1;i<=(todo);i++)
       {
           if((i&1)==0)
           {
               arr[i]=j;
               j++;
           }
       }



       for(int i=1;i<=n;i++)
        cout<<arr[i]<<' ';
       cout<<'\n';
   }

   return 0;
}