D. Super-Permutationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA permutation is a sequence n integers, where each integer from 1 to n appears exactly once. For example, [1], [3,5,2,1,4], [1,3,2] are permutations, while [2,3,2], [4,3,1], [0] are not.Given a permutation a, we construct an array b, where b_i = (a_1 + a_2 +~\dots~+ a_i) \bmod n.A permutation of numbers [a_1, a_2, \dots, a_n] is called a super-permutation if [b_1 + 1, b_2 + 1, \dots, b_n + 1] is also a permutation of length n.Grisha became interested whether a super-permutation of length n exists. Help him solve this non-trivial problem. Output any super-permutation of length n, if it exists. Otherwise, output -1.InputThe first line contains a single integer t (1 \le t \le 10^4) — the number of test cases. The description of the test cases follows.Each test case consists of a single line containing one integer n (1 \le n \le 2 \cdot 10^5) — the length of the desired permutation.The sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, output in a separate line:  n integers — a super-permutation of length n, if it exists.  -1, otherwise. If there are several suitable permutations, output any of them.ExampleInput
41236Output
1
2 1
-1
6 5 2 3 4 1
41236
1 2 1 -1 6 5 2 3 4 1
['constructive algorithms', 'math', '*1200']