CF1991B AND Reconstruction

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] $ .