E. XOR Guessingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis is an interactive problem. Remember to flush your output while communicating with the testing program. You may use fflush(stdout) in C++, system.out.flush() in Java, stdout.flush() in Python or flush(output) in Pascal to flush the output. If you use some other programming language, consult its documentation. You may also refer to the guide on interactive problems: https://codeforces.com/blog/entry/45307.The jury picked an integer x not less than 0 and not greater than 2^{14} - 1. You have to guess this integer.To do so, you may ask no more than 2 queries. Each query should consist of 100 integer numbers a_1, a_2, ..., a_{100} (each integer should be not less than 0 and not greater than 2^{14} - 1). In response to your query, the jury will pick one integer i (1 \le i \le 100) and tell you the value of a_i \oplus x (the bitwise XOR of a_i and x). There is an additional constraint on the queries: all 200 integers you use in the queries should be distinct.It is guaranteed that the value of x is fixed beforehand in each test, but the choice of i in every query may depend on the integers you send.OutputTo give the answer, your program should print one line ! x with a line break in the end. After that, it should flush the output and terminate gracefully.InteractionBefore giving the answer, you may submit no more than 2 queries. To ask a query, print one line in the following format: ? a_1 a_2 ... a_{100}, where every a_j should be an integer from the range [0, 2^{14} - 1]. The line should be ended with a line break character. After submitting a query, flush the output and read the answer to your query — the value of a_i \oplus x for some i \in [1, 100]. No integer can be used in queries more than once.If you submit an incorrect query (or ask more than 2 queries), the answer to it will be one integer -1. After receiving such an answer, your program should terminate immediately — otherwise you may receive verdict "Runtime error", "Time limit exceeded" or some other verdict instead of "Wrong answer".ExampleInput
0
32Output
? 3 5 6
? 32 24 37
! 5NoteThe example of interaction is not correct — you should sumbit exactly 100 integers in each query. Everything else is correct.Hacks are forbidden in this problem.
0
32
? 3 5 6 ? 32 24 37 ! 5
['bitmasks', 'interactive', 'math', '*1900']