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;
typedef long long ll;
typedef long double ld;
#ifdef APURBA
#include "DEBUG_TEMPLATE.h"
#else
#define HERE
#define debug(args...)
#endif
const int N = 2e5 +5;
const ll mod = 1e9+7;
typedef pair<int,int> pii;



void TEST_CASES(int cas)
{
    int n,k;
    cin>>n>>k;
//    if(k>n-2)
//    {
//        cout<<"-1\n";
//        return;
//    }
    vector<int>a;
    int now = 1 , last = n;
    a.push_back(now);
    now++;
    int cnt = k;
    while(a.size()<n)
    {
        if(cnt)
        {
            a.push_back(last);
            a.push_back(now);
            last--;
            now++;
            cnt--;
        }
        else{
            a.push_back(now);
            now++;
        }
    }
    if(cnt || a.size()!=n)
    {
        cout<<"-1\n";
        return;
    }
    for(int i:a)
    {
        cout<<i<<" ";
    }
    cout<<"\n";



}




/*
*/

int32_t main()
{
#ifndef APURBA
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#endif
    //freopen("input.txt","r",stdin);
    //freopen("out1.txt","w",stdout);
    int t=1,cas=0;
    cin>>t;
    while(t--)
    {
        TEST_CASES(++cas);
    }
    return 0;
}