#P1578I. Interactive Rays
Interactive Rays
Description
This is an interactive problem.
Your goal is to find a circle on a plane by shooting rays and getting the distance to the circle as a result.
Interactor has three hidden integer parameters that are determined in advance for each test, but which you don't know — , , and . are coordinates of the circle's center and is its radius. The absolute values of , , and do not exceed , and .
You can shoot rays that extend from the origin and go via a point with the integer coordinates you specify. For each ray, you get a distance from the ray to the circle or if the ray intersects the circle.
Interaction
The interaction starts with your program printing a query to the standard output and finishes when your program finds and prints the answer to the problem.
Each query has a form of "? ", where and are integers (; or ).
The interactor outputs a line with a single floating-point number — the distance between a query ray and a circle that is precise to by an absolute value.
Your program can make the next query, read the output, and so on. You are allowed to do at most queries. At the end of the interaction, print the answer line "! ", flush the output and exit.
Note, that the output of the interactor is actually rounded to the 10-th digit after a decimal point, so if you are stress-testing your solution locally, make sure that you also perform the corresponding rounding.