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.

Construct a good array, or report that no good arrays exist.

Input

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 $$$b_1, b_2, \ldots, b_{n - 1}$$$ ($$$0 \le b_i \lt 2^{30}$$$) — the elements of the array $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a single integer $$$-1$$$ if no good arrays exist.

Otherwise, output $$$n$$$ space-separated integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \lt 2^{30}$$$) — the elements of a good array $$$a$$$.

If there are multiple solutions, you may output any of them.

Note

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 $$$a=[3, 7, 5, 6, 3]$$$.

AND Reconstruction

Examples