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>
#define int long long
#define endl "\n"
using namespace std;

void solve(){
   int n,k;
   cin>>n>>k;
   if(n<=2&&k>0){
    cout<<-1<<endl;
    return;
   }
   if(n==k){
    cout<<-1<<endl;
    return;
   }
   if(k==0){
    for(int i=1;i<=n;i++){
        cout<<i<<" ";
    }
    cout<<endl;
    return;
   }
   if(n<2*k+1){
    cout<<-1<<endl;
    return;
   }
   int temp=0;
   vector<int>a(n);
   iota(a.begin(),a.end(),1);
   for(int i=1;i+1<n;i+=2){
    if(k){
        swap(a[i],a[i+1]);
        k--;
    }
   }

   for(int i=0;i<n;i++){
    cout<<a[i]<<" ";
   }
   cout<<endl;

}
int32_t main() {
  // your code goes here
  ios_base::sync_with_stdio(0); 
  cin.tie(0);
  int tc;
  cin>>tc;
  while(tc--){
    solve();
  }
  return 0;
}