CF1870B Friendly Arrays

You are given two arrays of integers — $ a_1, \ldots, a_n $ of length $ n $ , and $ b_1, \ldots, b_m $ of length $ m $ . You can choose any element $ b_j $ from array $ b $ ( $ 1 \leq j \leq m $ ), and for all $ 1 \leq i \leq n $ perform $ a_i = a_i | b_j $ . You can perform any number of such operations. After all the operations, the value of $ x = a_1 \oplus a_2 \oplus \ldots \oplus a_n $ will be calculated. Find the minimum and maximum values of $ x $ that could be obtained after performing any set of operations. Above, $ | $ is the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR), and $ \oplus $ is the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. This is followed by the description of the test cases. The first line of each test case contains two integers $ n $ and $ m $ ( $ 1 \leq n, m \leq 2 \cdot 10^5 $ ) — the sizes of arrays $ a $ and $ b $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \leq a_i \leq 10^9 $ ) — the array $ a $ . The third line of each test case contains $ m $ integers $ b_1, b_2, \ldots, b_m $ ( $ 0 \leq b_i \leq 10^9 $ ) — the array $ b $ . It is guaranteed that the sum of values of $ n $ and $ m $ across all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output $ 2 $ numbers: the minimum and maximum possible values of $ x $ after performing any set of operations.

In the first test case, if we apply the operation with element $ b_1 = 1 $ , the array $ a $ will become $ [1, 1] $ , and $ x $ will be $ 0 $ . If no operations are applied, then $ x = 1 $ . In the second test case, if no operations are applied, then $ x = 2 $ . If we apply the operation with $ b_1 = 1 $ , then $ a = [1, 1, 3] $ , and $ x = 3 $ .