This is an interactive problem. Additionally, hacks are disabled for this problem. There are two hidden integers (b) and (v) such that (b \in \{0,1\}) and (0 \le v \lt 2^{30}.) There is also a hidden operation (\mathrm{ty},) which is either (\&) or (|.) Here, (\&) denotes the bitwise AND operation . Additionally, (|) denotes the bitwise OR operation . Your goal is to guess (b.) The interaction proceeds as follows: First, you send a value (x) to the interactor, such that (0 \le x \lt 2^{30}). The interactor sends back (v\,\mathrm{ty}\,x). Formally, it will send back (o(v,x)), where ()o(v,x) = \begin{cases}v\,\&\,x & \mathrm{ty} = \& \\ v\,|\,x & \mathrm{ty} = |.\end{cases}() You then send two numbers (m_0) and (m_1), where (0 \le m_0, m_1 \lt 2^{30}.) Finally, the interactor will send back (m_b \oplus v,) where (\oplus) denotes the bitwise XOR operation . After the interaction, you have to output (b). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^5)). The description of the test cases follows. Note that this is the only initial input given. First, you need to output a single integer (x \, (0 \le x \lt 2^{30})) — the initial value to send to the interactor. In response, you will receive a single integer (o\,(0 \le o \lt 2^{30})) — the result (o(v,x)) of the operation (v\,\mathrm{ty}\,x.) Next, you will send a single line containing two integers (m_0, m_1\,(0 \le m_0, m_1 \lt 2^{30}).) Finally, receive a single integer (r\,(0 \le r \lt 2^{30})) — the value of (m_b \oplus v.) Note that the interactor is partially adaptive — in particular, the choice of (v) may be determined by the initial input (x), but all hidden values will be fixed after . After printing each query do not forget to output the end of line and flush(^{\text{∗}}) the output. Otherwise, you will ge