A permutation is a sequence n� integers, where each integer from 11 to n� appears exactly once. For example, , [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],  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� (1≤t≤1041≤�≤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� (1≤n≤2⋅1051≤�≤2⋅105) — the length of the desired permutation.
The sum of n� over all test cases does not exceed 2⋅1052⋅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.