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A. Array and Peaks

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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.

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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