#P1608B. Build the Permutation
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ID: 6176
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Build the Permutation
No submission language available for this problem.
Description
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.
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.
Samples
3
4 1 1
6 1 2
6 4 0
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.