A. Array and Peaks

Description

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 \(t\) \((1 \leq t \leq 100)\) — the number of test cases.

Then t lines follow, each containing two space-separated integers \(n\) \((1 \leq n \leq 100)\) and \(k\) \((0 \leq k \leq n)\) — 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.

standard input

5
1 0
5 2
6 6
2 1
6 1

standard output

1 
2 4 1 5 3 
-1
-1
1 3 6 5 4 2

Note

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 \((a_{4} \gt a_{3}, a_{4} \gt a_{5})\).