B. Build the Permutationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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.ExampleInput
3
4 1 1
6 1 2
6 4 0
Output
1 3 2 4
4 2 3 1 5 6
-1
NoteIn 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.
3
4 1 1
6 1 2
6 4 0

1 3 2 4 4 2 3 1 5 6 -1 
['constructive algorithms', 'greedy', '*1200']