| You are given an array $b$ of $n - 1$ integers. | |
| An array $a$ of $n$ integers is called good if $b_i = a_i \, \& \, a_{i + 1}$ for $1 \le i \le n-1$, where $\&$ denotes the [bitwise AND operator](https://en.wikipedia.org/wiki/Bitwise_operation#AND). | |
| Construct a good array, or report that no good arrays exist. | |
| Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of test cases follows. | |
| The first line of each test case contains a single integer $n$ ($2 \le n \le 10^5$) — the length of the array $a$. | |
| The second line of each test case contains $n - 1$ integers $b_1, b_2, \ldots, b_{n - 1}$ ($0 \le b_i < 2^{30}$) — the elements of the array $b$. | |
| It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$. | |
| For each test case, output a single integer $-1$ if no good arrays exist. | |
| Otherwise, output $n$ space-separated integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i < 2^{30}$) — the elements of a good array $a$. | |
| If there are multiple solutions, you may output any of them. | |
| In the first test case, $b = [1]$. A possible good array is $a=[5, 3]$, because $a_1 \, \& \, a_2 = 5 \, \& \, 3 = 1 = b_1$. | |
| In the second test case, $b = [2, 0]$. A possible good array is $a=[3, 2, 1]$, because $a_1 \, \& \, a_2 = 3 \, \& \, 2 = 2 = b_1$ and $a_2 \, \& \, a_3 = 2 \, \& \, 1 = 0 = b_2$. | |
| In the third test case, $b = [1, 2, 3]$. It can be shown that no good arrays exist, so the output is $-1$. | |
| In the fourth test case, $b = [3, 5, 4, 2]$. A possible good array is $a=[3, 7, 5, 6, 3]$. |