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.