CF2119E And Constraint

[wowaka & Hatsune Miku - Tosenbo](https://www.youtube.com/watch?v=uxNoOPetZ6g) You are given a sequence $ a $ of length $ n-1 $ and a sequence $ b $ of length $ n $ . You can perform the following operation any number of times (possibly zero): - choose an index $ 1 \le i \le n $ and increment $ b_i $ by $ 1 $ (i.e., set $ b_i \leftarrow b_i + 1 $ ). Your goal is to perform the minimum number of operations such that for every $ 1 \le i \le n-1 $ , the condition $ b_i \, \& \, b_{i+1} = a_i $ holds, where $ \& $ denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). If it is impossible to satisfy the condition, report it as well.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ). The second line contains $ n-1 $ integers $ a_1, a_2, \ldots, a_{n-1} $ ( $ 0 \le a_i < 2^{29} $ ). The third line contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 0 \le b_i < 2^{29} $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, you need to output only one integer. If the goal can be achieved, output one integer — the minimum number of operations required. Otherwise, output $ -1 $ .

In the first test case, one of the optimal strategies is to use $ 4 $ operations to make $ b = [1,5,4,4] $ , which satisfies all the conditions. We can prove that it is impossible to use fewer than $ 4 $ operations. In the second test case, since $ b_1 \, \& \, b_2 = 4 $ and $ b_2 \, \& \, b_3 =0 $ , then $ b_3 \, \& \, 4 =0 $ . However, we require that $ b_3 \, \& \, b_4 =4 $ , which means it is impossible to satisfy all the conditions.