A. Farmer John's Challenge
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Trade Winds - Patrick Deng
⠀

Let's call an array $$$a$$$ sorted if $$$a_1 \leq a_2 \leq \ldots \leq a_{n - 1} \leq a_{n}$$$.

You are given two of Farmer John's favorite integers, $$$n$$$ and $$$k$$$. He challenges you to find any array $$$a_1, a_2, \ldots, a_{n}$$$ satisfying the following requirements:

  • $$$1 \leq a_i \leq 10^9$$$ for each $$$1 \leq i \leq n$$$;
  • Out of the $$$n$$$ total cyclic shifts of $$$a$$$, exactly $$$k$$$ of them are sorted.$$$^\dagger$$$

If there is no such array $$$a$$$, output $$$-1$$$.

$$$^\dagger$$$The $$$x$$$-th ($$$1 \leq x \leq n$$$) cyclic shift of the array $$$a$$$ is $$$a_x, a_{x+1} \ldots a_n, a_1, a_2 \ldots a_{x - 1}$$$. If $$$c_{x, i}$$$ denotes the $$$i$$$'th element of the $$$x$$$'th cyclic shift of $$$a$$$, exactly $$$k$$$ such $$$x$$$ should satisfy $$$c_{x,1} \leq c_{x,2} \leq \ldots \leq c_{x, n - 1} \leq c_{x, n}$$$.

For example, the cyclic shifts for $$$a = [1, 2, 3, 3]$$$ are the following:

  • $$$x = 1$$$: $$$[1, 2, 3, 3]$$$ (sorted);
  • $$$x = 2$$$: $$$[2, 3, 3, 1]$$$ (not sorted);
  • $$$x = 3$$$: $$$[3, 3, 1, 2]$$$ (not sorted);
  • $$$x = 4$$$: $$$[3, 1, 2, 3]$$$ (not sorted).
Input

The first line contains $$$t$$$ ($$$1 \leq t \leq 10^3$$$) — the number of test cases.

Each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq k \leq n \leq 10^3$$$) — the length of $$$a$$$ and the number of sorted cyclic shifts $$$a$$$ must have.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^3$$$.

Output

For each test case, print a single line:

  • if there is a valid array $$$a$$$, output $$$n$$$ integers, representing $$$a_1, a_2, \ldots, a_{n}$$$;
  • otherwise, output $$$-1$$$.

If there are multiple solutions, print any of them.

Example
Input
3
2 2
3 1
3 2
Output
1 1
69420 69 420
-1
Note

In the first testcase, $$$a = [1, 1]$$$ satisfies $$$n = 2, k = 2$$$:

The two cyclic shifts of $$$a$$$ are $$$[a_1, a_2]$$$ and $$$[a_2, a_1]$$$, which are both $$$[1, 1]$$$ and are sorted.

In the second testcase, $$$a = [69\,420, 69, 420]$$$ satisfies $$$n = 3, k = 1$$$:

The three cyclic shifts of $$$a$$$ are $$$[a_1, a_2, a_3]$$$, $$$[a_2, a_3, a_1]$$$, $$$[a_3, a_1, a_2]$$$, which are $$$[69\,420, 69, 420]$$$, $$$[69, 420, 69\,420]$$$, and $$$[420, 69\,420, 69]$$$, respectively.

Only $$$[69, 420, 69\,420]$$$ is sorted.