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 BOOST ios_base::sync_with_stdio(false); cin.tie(NULL);
#define precision(x); cout<<fixed<<setprecision(x);
#define lli long long int
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define all(v) v.begin(),v.end()
#define desc greater<int>()
#define mod 1000000007

using namespace std;

int main()
{
    BOOST
    int t;
    cin>>t;
    while(t--){
    	int n,k;
    	cin>>n>>k;
    	int maxm=(n%2==0)?((n/2)-1):n/2;
    	if(k>maxm){
    		cout<<-1<<endl;
    		continue;
    	}
    	int arr[n];
    	int x=1,y=n;
    	for(int i=0; i<n; i++){
    		if(i%2==0){
    			arr[i]=x;
    			x++;
    		}else{
    			arr[i]=y;
    			y--;
    		}
    	}
    	int valK=n-k+1;
    	int indK=2*k-1;
    	valK--;
    	for(int i=indK+1; i<n; i++){
    		arr[i]=valK;
    		valK--;
    	}
    	for(int i=0; i<n; i++){
    		cout<<arr[i]<<" ";
    	}
    	cout<<endl;
    }
    return 0;
}