Draw A Perfect Circle

Dongguri is practicing the circle challenge. In this challenge, you swing your arm like a compass and draw a circle on a chalkboard.

Dongguri found it hard to tell how close his drawing is to a circle, so he asked you to write a program that computes its accuracy.

Dongguri's drawing is represented by $N$ points, and the width of the band that contains the points, $K$, is given.

The accuracy is computed as follows.

• For any radius $R$, define $cnt(R)$ as the number of points whose distance from the origin is at least $\max(0,R-\frac{K}{2})$ and at most $R+\frac{K}{2}$. (The distance between two points with x-coordinate difference $p$ and y-coordinate difference $q$ is defined as $\sqrt{p^2+q^2}$.)
• The accuracy is $\frac{100}{N}\times \max_{R \ge 0} cnt(R)$, where $R$ is a real number.

Help Dongguri draw a perfect circle!

The first line contains two integers $N$ ($1\leq N \leq 200\,000$) and $K$ ($1\leq K \leq 20\,000$), separated by a space. Both $N$ and $K$ are integers.

The next $N$ lines each contain two integers $x_i$ and $y_i$, the coordinates of the $i$-th point. ($-10\,000 \le x_i, y_i \le 10\,000$)

All point positions are guaranteed to be distinct.

Print the accuracy of Dongguri's drawing.

An answer is accepted if its absolute or relative error from the correct answer is at most $10^{-6}$.

The absolute error is the difference between the correct answer and your output. The relative error is the absolute error divided by the correct answer.