Codeforces Round 867 (Div. 3) |
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Finished |
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:
If there are several suitable permutations, output any of them.
41236
1 2 1 -1 6 5 2 3 4 1
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