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;
int t, n, a[1000], k;
int main()
{
    cin >> t;
    while(t--)
    {
        cin >> n >> k;
        if(k <= (n - 1)/2)
        {
            int spt = 0, spt1 = k + 1;
            for(int i = 1; i <= 2*k + 1; i++)
            {
                if(i%2 == 1)
                    a[i] = ++spt;
                else a[i] = ++spt1;
            }
            for(int i = 2*k + 2; i <= n; ++i)
                a[i] = ++spt1;
            for(int i = 1; i <= n; ++i)
                cout << a[i] << " ";
            cout << "\n";
        }
        else cout << -1 << "\n";
    }
    return 0;
}