XOR = Average
Description
You are given an integer $n$. Find a sequence of $n$ integers $a_1, a_2, \dots, a_n$ such that $1 \leq a_i \leq 10^9$ for all $i$ and $$a_1 \oplus a_2 \oplus \dots \oplus a_n = \frac{a_1 + a_2 + \dots + a_n}{n},$$ where $\oplus$ represents the bitwise XOR.
It can be proven that there exists a sequence of integers that satisfies all the conditions above.
The first line of input contains $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first and only line of each test case contains one integer $n$ ($1 \leq n \leq 10^5$) — the length of the sequence you have to find.
The sum of $n$ over all test cases does not exceed $10^5$.
For each test case, output $n$ space-separated integers $a_1, a_2, \dots, a_n$ satisfying the conditions in the statement.
If there are several possible answers, you can output any of them.
Input
The first line of input contains $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first and only line of each test case contains one integer $n$ ($1 \leq n \leq 10^5$) — the length of the sequence you have to find.
The sum of $n$ over all test cases does not exceed $10^5$.
Output
For each test case, output $n$ space-separated integers $a_1, a_2, \dots, a_n$ satisfying the conditions in the statement.
If there are several possible answers, you can output any of them.
3
1
4
3
69
13 2 8 1
7 7 7
Note
In the first test case, $69 = \frac{69}{1} = 69$.
In the second test case, $13 \oplus 2 \oplus 8 \oplus 1 = \frac{13 + 2 + 8 + 1}{4} = 6$.