33430번 - Operator Precedence 스페셜 저지다국어

Randias is facing his primary school homework:

Find a nonzero integer sequence $a$ of length $2n$ satisfying

\begin{alignat*}{26} (&a_1 &\times& &a_2&)&+&(&a_3& &\times& &a_4&)&+& & \ldots & & &+&(&a_{2n-1}& &\times& a_{2n}&)\\ = &a_1 &\times&(&a_2& &+& &a_3&)&\times&(&a_4& &+& a_5)\times& \ldots & \times&(a_{2n-2} &+& &a_{2n-1}&)&\times& a_{2n}&\ne 0\text{.} \end{alignat*}

In shorter form, $\sum\limits_{i=1}^n a_{2i-1} a_{2i} = a_1 a_{2n} \prod\limits_{i=2}^{n} (a_{2i-2} + a_{2i-1}) \ne 0$.

Of course, Randias knows how to solve it. But he wants to give you a test. Can you solve the question above?

Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^5$) denoting the number of test cases.

For each test case, the only line contains a single integer $n$ ($2 \le n \le 10^5$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

For each test case, output one line with $2 n$ integers: $a_1, a_2, \ldots, a_{2n}$ ($1 \le |a_i| \le 10^{10}$).

It can be shown that the answer always exists.

If there are several possible answers, output any one of them.