Description:
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 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 $$$0 \le a,b<2^{30}$$$.
Input Format:
See the interaction section.
Output Format:
To print the answer, print "! a b" (without quotes). Don't forget to flush the output after printing the answer.
Note:
In the sample:
The hidden numbers are $$$a=3$$$ and $$$b=1$$$.
In the first query: $$$3 \oplus 2 = 1$$$ and $$$1 \oplus 1 = 0$$$, so the answer is 1.
In the second query: $$$3 \oplus 1 = 2$$$ and $$$1 \oplus 2 = 3$$$, so the answer is -1.
In the third query: $$$3 \oplus 2 = 1$$$ and $$$1 \oplus 0 = 1$$$, so the answer is 0.
Then, we printed the answer.