P9635 "yyOI R1" youyou's XOR

youyou is very weak, but he really likes constructing strange sequences.

This problem uses **Special Judge**. youyou likes sequences very much, so he wants you to construct a **positive integer** sequence $\{a_i\}$ of length $n$. youyou likes [XOR](https://oi-wiki.org/math/bit/#%E4%B8%8E%E6%88%96%E5%BC%82%E6%88%96), so he requires the constructed sequence to satisfy $a_1 \oplus a_2 \oplus a_3 \oplus \cdots \oplus a_{n-1} \oplus a_n = n$ (where $\oplus$ denotes XOR). youyou really hates identical numbers, so he requires that all numbers in the sequence are **pairwise distinct**. But youyou does not want the numbers in this sequence to be too large, so he requires that the sum of all numbers in the sequence does not exceed $n^2$, i.e., $\displaystyle\sum_{i=1}^n a_i \le n^2$. Now you need to construct a sequence that satisfies all of youyou's requirements. If there is no solution, output `-1`. If there are multiple answers, output any one of them. You need to answer $T$ test cases.

The first line contains a positive integer $T$. The next $T$ lines each contain an integer $n$, meaning you need to construct a required sequence of length $n$.

Output $T$ lines in total. If the $i$-th line corresponds to constructing a sequence of length $n$, then output exactly $n$ numbers on that line, representing your constructed sequence. Note that every number in the sequence must be a **positive integer**. If such a sequence cannot be constructed, output `-1` on this line.

### Sample Explanation For $n = 1$, one feasible solution is $\{1\}$. For $n = 2$, one feasible solution is $\{3,1\}$. For $n = 5$, one feasible solution is $\{1,4,5,3,6\}$, because $1 ⊕ 4 ⊕ 5 ⊕ 3 ⊕ 6 = 5$, and $1+4+5+3+6 =19\le 5^2$, and all numbers in the sequence are also pairwise distinct. ### Constraints For $5\%$ of the testdata, $n \le 5$. For $15\%$ of the testdata, $n \le 10$. For $40\%$ of the testdata, $n \le 1000$. For $70\%$ of the testdata, $n \le 10^5$. For $100\%$ of the testdata, $1 \le n \le 5 × 10^5$, and $1 \le T \le 10$. Translated by ChatGPT 5