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;
 
#define rep(i,a,b) for(int i=a;i<b;i++)
#define ll long long int
#define test() int tt; cin>>tt; while(tt--) 
#define fst_io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define endl '\n'
#define lg 1000000000
#define vec vector<int>
void arrInput(int a[],int n){rep(i,0,n) cin>>a[i];}

void solve()
{
  int n,k;
  cin>>n>>k;
  vector<int> res;
  int low=1,high=n-k+1,p=n-k;
  while(high<=n) 
  {
    res.push_back(low);
    res.push_back(high);	
    low++;
    high++;
  }
  for(int i=low; i<=p; i++) res.push_back(i);
  int c=0;
  for(int i=1; i<res.size()-1; i++)
  {
  	if(res[i]>res[i-1] && res[i]>res[i+1]) c++;
  }
  if(c>=k)
  {
    for(auto i:res) cout<<i<<" ";
    cout<<endl;	
  }
  else cout<<"-1\n";
}

int main()
{
  test() solve();
}