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;
const int INF = INT_MAX;
#define ll long long
#define tie ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define w(t) int t;cin>>t;while(t--)
#define inf 1e18
#define l length()
void solve(){
}
int main(){
    tie
    w(t){
        int n,k;
        cin>>n>>k;
        if((n<3 && k!=0) || n<=k || (n-1)/2<k) {cout<<"-1\n";continue;}
        if(k==0){
            for(int i=1;i<=n;i++) cout<<i<<" ";
            cout<<"\n";
            continue;
        }
        int i=1;
        cout<<i<<" "<<i+2<<" "<<i+1<<" ";
        i=4;n-=3;
        k--;
        while(k!=0){
            cout<<i+1<<" "<<i<<" ";
            k--;i+=2;n-=2;
        }
        while(n!=0) { cout<<i<<" ";i++;n--;}
        cout<<"\n";
    }
}