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 <iostream>
#include <vector>

using namespace std;

int main() {
    // freopen("input.txt","r",stdin);
    int tc_num;
    cin>>tc_num;
    for(int k=0;k<tc_num;k++) {
        int per_num, peak_num;
        vector<int> v;
        cin>>per_num>>peak_num;

        if(peak_num > (per_num-1)/2) {
            cout<<-1<<'\n';
            continue;
        }
        int peak_count = 0;
        for(int i=1;i<=per_num/2;i++) {
            if(peak_count>=peak_num) {
                break;
            }
            v.push_back(i);
            v.push_back(per_num+1-i);
            peak_count++;
        }
        for(int i=peak_count+1;i<per_num+1-peak_num;i++) {
            v.push_back(i);
        }
        for(int i=0;i<v.size();i++) {
            cout<<v[i]<<' ';
        }
        cout<<'\n';
    }
}