A12174 | Ehab and another another xor problem

This is an interactive problem!

Ehab plays a game with Laggy. Ehab has 2 hidden integers $(a,b)$ . Laggy can ask a pair of integers $(c,d)$ and Ehab will reply with:

- 1 if $a \oplus c>b \oplus d$ .
- 0 if $a \oplus c=b \oplus d$ .
- -1 if $a \oplus c<b \oplus d$ .

Operation $a \oplus b$ is the [bitwise-xor operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of two numbers $a$ and $b$ .

Laggy should guess $(a,b)$ with at most 62 questions. You'll play this game. You're Laggy and the interactor is Ehab.

It's guaranteed that $0 \le a,b<2^{30}$ .

See the interaction section.

To print the answer, print "! a b" (without quotes). Don't forget to flush the output after printing the answer.

Interaction

To ask a question, print "? c d" (without quotes). Both $c$ and $d$ must be non-negative integers less than $2^{30}$ . Don't forget to flush the output after printing any question.

After each question, you should read the answer as mentioned in the legend. If the interactor replies with -2, that means you asked more than 62 queries and your program should terminate.

To flush the output, you can use:-

- fflush(stdout) in C++.
- System.out.flush() in Java.
- stdout.flush() in Python.
- flush(output) in Pascal.
- See the documentation for other languages.

Hacking:

To hack someone, print the 2 space-separated integers $a$ and $b$ $(0 \le a,b<2^{30})$ .