Super-Permutation solution codeforces

A permutation is a sequence n integers, where each integer from 11 to n appears exactly once. For example, [1][1][3,5,2,1,4][3,5,2,1,4][1,3,2][1,3,2] are permutations, while [2,3,2][2,3,2][4,3,1][4,3,1][0][0] are not.

Given a permutation a, we construct an array b, where bi=(a1+a2+  +ai)modn��=(�1+�2+ … +��)mod�.

A permutation of numbers [a1,a2,,an][�1,�2,…,��] is called a super-permutation if [b1+1,b2+1,,bn+1][�1+1,�2+1,…,��+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 1−1.


The first line contains a single integer t (1t1041≤�≤104) — the number of test cases. The description of the test cases follows.

Each test case consists of a single line containing one integer n (1n21051≤�≤2⋅105) — the length of the desired permutation.

The sum of n over all test cases does not exceed 21052⋅105.


For each test case, output in a separate line:

  • n integers — a super-permutation of length n, if it exists.
  • 1−1, otherwise.

If there are several suitable permutations, output any of them.

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