Preparando MOJI
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.
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 $$$10^5$$$.
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.
3 4 1 1 6 1 2 6 4 0
1 3 2 4 4 2 3 1 5 6 -1
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.
Informação
Provedor Codeforces
Código CF1608B
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Datas 09/05/2023 10:19:41
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