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:
//doit4von
#include<bits/stdc++.h>
using namespace std;
const int N=1e6+5;
typedef long long ll;
void google(int tc)
{
    cout<<"Case #"<<tc<<": ";
}
bool palindrome(const string &s) {
    int n = s.length();
    for(int i = 0; i < n; i++) {
        if(s[i] != s[n - i - 1]) return false;
    }
    return true;
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t;
cin>>t;
while(t--)
{
   int n,k;
   cin>>n>>k;
   if(k*2<=n-1)
   {
       int ar[n];
       int i;
       int high=n;
       int low=1;
       for(i=0;i<k*2;i+=2)
       {
           ar[i]=low++;
           ar[i+1]=high--;
       }
       for(int j=2*k;j<n;j++)
       ar[j]=low++;;
       for( i=0;i<n;i++)
       cout<<ar[i]<<" ";
       cout<<"\n";
   }
   else
   cout<<"-1\n";
}
}