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 ll long long
using namespace std;
const ll MOD=1000000007;
int main(){
int t;cin>>t;
while(t--){
	int n,k;cin>>n>>k;
	int a[n];
	for(int i=0;i<n;i++){
		a[i]=i+1;
	}
	if(n%2==0){
		if(k>(n/2 -1)){
			cout<<-1<<"\n";
		}
		else{
			int i=1;
			while(k>0&&i<n){
				swap(a[i],a[i+1]);
				i+=2;k--;
			}
			for(int i=0;i<n;i++) cout<<a[i]<<" ";
			cout<<"\n";
		}
	}
	else{
		if(k>(n/2)){cout<<-1<<"\n";}
		else{
			int i=1;
			while(k>0&&i<n){
				swap(a[i],a[i+1]);
				i+=2;k--;
			}
			for(int i=0;i<n;i++) cout<<a[i]<<" ";
			cout<<"\n";
		}
	}
}
}