D. Super-Permutation
constructive algorithms; math
A 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 \(-1\).
The 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 \(2 \cdot 10^5\).
For 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.