P10369 "LAOI-4" Mex Tower (Easy ver.)

**The difference between this problem and the Hard Version is that this problem requires you to output a valid construction.**

Define $\operatorname{mex}(x, y)$ as the smallest **natural number** that does not appear in the set $\{x, y\}$. For example, $\operatorname{mex}(1, 5) = 0$ and $\operatorname{mex}(3, 0) = 1$. Next, we define one operation on a natural number sequence $a_1 \dots a_n$ as replacing sequence $a$ with a sequence $b_1 \dots b_{n-1}$ of **length $\bm{n - 1}$**, where $b_i = \operatorname{mex}(a_i, a_{i+1})$. You need to construct a natural number sequence $a_1 \dots a_n$ of length $n$, satisfying $0 \leq a_i \leq 10^9$, and then perform $n - 1$ operations on it. Obviously, in the end the sequence $a$ will have only one number left, and you need to maximize the value of this number. If there are multiple possible sequences, you may output any valid construction.

**This problem contains multiple test cases.** The first line contains a positive integer $T$, the number of test cases. For each test case, there is only one line containing a positive integer $n$.

For each test case, output one line with $n$ integers, representing the sequence $a_1 \dots a_n$ you constructed.

### Sample Explanation For $n = 2$, after applying the operation to $[0, 1]$, we will clearly get $[2]$. It can be proven that this is the maximum answer we can obtain. Other valid outputs such as $[1, 0]$ can also work. For $n = 5$ and $n = 7$, we cannot give you a clear answer for now. ### Constraints **"This problem uses bundled tests"** | $\text{Subtask}$ | $\sum n \le$| Special Property | Total Score | | :--------------: | :-----: |:-----: | :--------: | | $1$ | $10$ | None | $5$ | | $2$ | $10^5$ | $\text{A}$ | $15$ | | $3$ | $10^5$ | $\text{B}$ | $15$ | | $4$ | $50$ | $n \le 25$ | $10$ | | $5$ | $10^3$ | None | $20$ | | $6$ | $10^6$ | None | $35$ | Special property $\text{A}$: it is guaranteed that $n \equiv 3 \pmod 4$. Special property $\text{B}$: it is guaranteed that $n \equiv 2 \pmod 4$. For all testdata, it is guaranteed that $1 \leq T \leq 10^4$, $n > 1$, and $\sum n \leq 10^6$. Translated by ChatGPT 5