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;
#include<cstring>
#include<vector>
typedef long long int ll;
typedef long double ld;
typedef double db;

int main()
{           ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
    ll tt;cin>>tt;

    for(ll ii=0;ii<tt;ii++)
    {
   ll n,k;cin>>n>>k;
   ll a[n];
    for(ll i=0;i<n;i++)
    {
        a[i]=i+1;
    }
    if(  k==0 )
    {
        for(ll i=0;i<n;i++)
    {
        cout<<a[i]<<" ";
    } cout<<endl;
    }

   else  if( n<=2 && k!=0 )
    {
        cout<<-1<<endl;
    }
    else {
    ll p=n%2==0?n/2-1:n/2;
    if( p<k  )
    {
        cout<<-1<<endl;
    }
    else
    { ll t=0;
        for(ll i=n-1;i>=0;i=i-2  )
        {
            swap( a[i],a[i-1]  );t++;
            if(t==k ){break; }
        }
        for(ll i=0;i<n;i++)
    {
        cout<<a[i]<<" ";
    } cout<<endl;
    }

    }

    }
return 0;
}