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I. Interactive Rays
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

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 — $$$x_c$$$, $$$y_c$$$, and $$$r_c$$$. $$$(x_c, y_c)$$$ are coordinates of the circle's center and $$$r_c$$$ is its radius. The absolute values of $$$x_c$$$, $$$y_c$$$, and $$$r_c$$$ do not exceed $$$10^5$$$, and $$$1 \leq r_c \leq \sqrt{x_c^2 + y_c^2} - 1$$$.

You can shoot rays that extend from the origin $$$(0,0)$$$ and go via a point $$$(x_q,y_q)$$$ with the integer coordinates you specify. For each ray, you get a distance from the ray to the circle or $$$0$$$ 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 "? $$$x_q$$$ $$$y_q$$$", where $$$x_q$$$ and $$$y_q$$$ are integers ($$$|x_q|, |y_q| \le 10^6$$$; $$$x_q \ne 0$$$ or $$$y_q \ne 0$$$).

The interactor outputs a line with a single floating-point number — the distance between a query ray and a circle that is precise to $$$10^{-10}$$$ by an absolute value.

Your program can make the next query, read the output, and so on. You are allowed to do at most $$$60$$$ queries. At the end of the interaction, print the answer line "! $$$x_c$$$ $$$y_c$$$ $$$r_c$$$", 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.

Example
Input
? 0 -10

? 10 -10

? 10 0

? 10 10

? 10 20

? 10 30

! 20 10 10
Output
12.360679775

11.2132034356

0.0

0.0

3.416407865

5.8113883008
Note
Illustration of the queries from the example interaction.