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 — $$$x_c$$$, $$$y_c$$$, 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.
Input Format:
None
Output Format:
None
Note:
Illustration of the queries from the example interaction.