Codeforces Round 867 (Div. 3) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

constructive algorithms

math

*1200

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. Super-Permutation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$-1$$$.

Input

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 $$$2 \cdot 10^5$$$.

Output

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.

Example

Input

41236

Output

1 2 1 -1 6 5 2 3 4 1

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/30/2023 20:58:29 (j2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|