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 fast_io ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define ll long long int
#define f(i,x,n) for(long long int i=x;i<n;i++)
#define fr(i,x,n) for(long long int i=n-1;i>=x;i--)
#define pb push_back
#define mp make_pair
#define mod 1000000007




int main(){
    fast_io
    
    int t; cin>>t;
    while(t--){
        int n,k;
        cin>>n>>k;
        
        if(n&1 && k>n/2 ) cout<<-1<<endl;
        else if(n%2==0 && k>n/2 -1) cout<<-1<<endl;
        else{
        vector <int> v(n,-1);
        int j=n,m=n-k;
        for(int i=1;i<n && j>n-k;i+=2){
            v[i]=j;
            j--;
        }
        
        f(i,0,n){
            if(v[i]==-1){
                v[i]=m;
                m--;
            }
        }
        
        f(i,0,n) cout<<v[i]<<" ";
        cout<<endl;
        
        }
        
    }

return 0;
}