B. XOR = Average
constructive algorithms
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.
In the first test case, \(69 = \frac{69}{1} = 69\).In the second test case, \(13 \oplus 2 \oplus 8 \oplus 1 = \frac{13 + 2 + 8 + 1}{4} = 6\).