A16241. 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 $x = 3$ .