Background

You are the astrology magic fairy in the Magic Fairy Castle.

Problem Description

The Magic Fairy Queen’s gem was stolen by the ancient "Gunalab Dark God". The "Gunalab Dark God" is hiding in any one of the $n$ domes in the Magic Fairy Castle. These $n$ domes are numbered from $1$ to $n$. The $i$-th dome can be assigned a magic power value $a_i$, and $a_i$ must be an integer.

If the sum of the magic power values of all domes is $0$ and their product is $n$, then we say that in this situation, the "Gunalab Dark God" can be found easily.

The Magic Fairy Queen asks the astrology magic fairy to find an assignment of magic power values so that the "Gunalab Dark God" can be found easily.

Input Format

This problem has multiple test cases.

The first line contains a positive integer $T$, representing the number of test cases.

The next $T$ lines each contain one integer $n$.

Output Format

Output $T$ lines. The $i$-th line should contain the answer for the $i$-th test case.

If there is a solution, output one line with $n$ integers representing a constructed sequence of magic power values. Otherwise, output w33zAKIOI.

This problem uses Special Judge, so you only need to output one valid sequence.

2
4
114513

1 -1 2 -2
w33zAKIOI

1
1

w33zAKIOI

Hint

Sample 1 Explanation

$1 + (-1) + 2 + (-2) = 0$, $1 \times (-1) \times 2 \times (-2) = 4$.

Constraints

This problem uses bundled tests.

• Subtask 1 (5 pts): $n \le 1$
• Subtask 2 (20 pts): $n, \sum n \le 100$
• Subtask 3 (75 pts): no special constraints.

For $100\%$ of the testdata, $1 \le n \le 10^6$, $\sum n \le 5 \times 10^6$, $1 \le T \le 10^5$.

This problem uses Special Judge, so you only need to output one valid sequence.

Translated by ChatGPT 5