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 . 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.