B. XOR = Average
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Example
Input
3
1
4
3
Output
69
13 2 8 1
7 7 7
Note

In the first test case, $$$69 = \frac{69}{1} = 69$$$.

In the second test case, $$$13 \oplus 2 \oplus 8 \oplus 1 = \frac{13 + 2 + 8 + 1}{4} = 6$$$.