This is an interactive problem.
We have conceived a line in the form of $$$y = kx + b$$$. Your task is to deduce this line.
You can make queries, in one question you specify a point ($$$x, y$$$) and receive in return the shortest distance from the point to the line.
Can you manage in no more than $$$5$$$ queries?
It is guaranteed that ($$$-100 \le k, b \le 100$$$).
You can start making queries right away. To do this, output:
on a separate line. After making a query, read a non-negative real number $$$d$$$ with precision up to $$$20$$$ digits – the shortest distance from the point you provided to the line. If you make an incorrect query or exceed the set limit of $$$5$$$ queries, you will receive the number $$$-1$$$ in response, in which case your program should immediately terminate.
To output the answer, output
on a separate line. Your answer will be considered correct if the relative or absolute error of the coefficients $$$k$$$ and $$$b$$$ is no more than $$$10^{-3}$$$.
After any output, do not forget to output a newline and flush the output buffer. Otherwise, you will receive the verdict Idleness limit exceeded. To flush the buffer, use:
1.41421356237309504876 0.70710678118654752438
? 0.000 0.000 ? 0.000 1.000 ! 1.0000 2.0001
0.00000000000000000000 0.00000000000000000000 5.00000000000000000000 5.00000000000000000000 2.50000000000000000000
? 0 5 ? 5 5 ? 5 0 ? 0 0 ? 2.5 2.5 ! 0.000000011 5.00000003