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:
using namespace std;
#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <iomanip>
#include <cmath>
#include <fstream>
#include <queue>
#include <deque>
#include <unordered_set>
#include <cstring>  
#include <set>  


int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    long long T;
    cin >> T;
    while (T--) {
        long long n, k;
        cin >> n >> k;
        if ((n / 2) - (n % 2 == 0) < k) {
            cout << -1 << endl;
        }
        else {
            for (long long j = 1, m = n, i = 1; i <= n; i++) {
                if (k > 0 and i % 2 == 0) {
                    cout << m << " ";
                    m--;
                    k--;
                    continue;
                }
                cout << j << " ";
                j++;

            }
            cout << endl;
        }

    }




    return 0;
}