B. Build the Permutation
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given three integers $$$n, a, b$$$. Determine if there exists a permutation $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$, such that:

  • There are exactly $$$a$$$ integers $$$i$$$ with $$$2 \le i \le n-1$$$ such that $$$p_{i-1} < p_i > p_{i+1}$$$ (in other words, there are exactly $$$a$$$ local maximums).

  • There are exactly $$$b$$$ integers $$$i$$$ with $$$2 \le i \le n-1$$$ such that $$$p_{i-1} > p_i < p_{i+1}$$$ (in other words, there are exactly $$$b$$$ local minimums).

If such permutations exist, find any such permutation.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of test cases follows.

The only line of each test case contains three integers $$$n$$$, $$$a$$$ and $$$b$$$ ($$$2 \leq n \leq 10^5$$$, $$$0 \leq a,b \leq n$$$).

The sum of $$$n$$$ over all test cases doesn't exceed $$$10^5$$$.

Output

For each test case, if there is no permutation with the requested properties, output $$$-1$$$.

Otherwise, print the permutation that you are found. If there are several such permutations, you may print any of them.

Example
Input
3
4 1 1
6 1 2
6 4 0
Output
1 3 2 4
4 2 3 1 5 6
-1
Note

In the first test case, one example of such permutations is $$$[1, 3, 2, 4]$$$. In it $$$p_1 < p_2 > p_3$$$, and $$$2$$$ is the only such index, and $$$p_2> p_3 < p_4$$$, and $$$3$$$ the only such index.

One can show that there is no such permutation for the third test case.