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2 초 512 MB51120.000%

문제

You are given an integer $K$ such that $1 \le K \le 10^6$. Construct any array $A$ of numbers for which the following properties hold:

  • The size of $A$ is between $1$ and $30$;
  • All elements are integers between $-10^{16}$ and $10^{16}$;
  • Let $N$ be the size of $A$. Then there are exactly $K$ subsets $S$ (possibly empty) of set $\{1, 2, \ldots, N\}$ for which $\sum_{i \in S} A_i = 0$.

It can be shown that, under the constraints above, such array $A$ always exists.

입력

The first line contains a single integer $t$ ($1 \le t \le 1000$), the number of test cases.

Each of the next $t$ lines contains a single integer $K$ ($1 \le K \le 10^6$).

출력

For each test case, on the first line, output a single integer $N$ ($1 \le N \le 30$), the size of your array.

On the second line, output $N$ integers $A_1, A_2, \ldots, A_N$ ($-10^{16} \le A_i \le 10^{16}$), the elements of the array.

예제 입력 1

2
3
16

예제 출력 1

5
2021 -1000 -1021 -2000 -21
4
0 0 0 0

힌트

Note that the elements of the array don't have to be distinct.