A team of space archaeologists has discovered a cluster of $N$ ancient energy monoliths on a two-dimensional planetary plane. The position of the $i$-th monolith is given by integer coordinates $(x_i, y_i)$. To conduct research safely without triggering an energy chain reaction, they need to deploy a straight-line laser barrier $L$.
Due to the unstable gravitational fluctuations at the coordinate origin $(0,0)$, the barrier $L$ cannot be placed too close to the center. Specifically, the perpendicular distance from the origin $(0,0)$ to the line $L$ must be at least $R$.
The **hazard level** of the barrier setup is defined as the maximum perpendicular distance from any of the $N$ monoliths to the line $L$. The archaeologists want to find a valid line $L$ that minimizes this hazard level. Can you help them compute the minimum possible hazard level?
The first line contains two integers $N$ and $R$ ($3 \le N \le 10^5$, $0 \le R \le 10^6$) — the number of monoliths and the minimum allowed distance from the origin to the barrier.
Each of the next $N$ lines contains two integers $x_i$ and $y_i$ ($-10^6 \le x_i, y_i \le 10^6$) — the coordinates of the $i$-th monolith.
It is guaranteed that the monoliths are not all collinear, and no monolith is located exactly at the origin.
Output a single floating-point number representing the minimum possible hazard level. Your answer will be accepted if its absolute or relative error does not exceed $10^{-9}$.
4 0 2 2 -2 2 -2 -2 2 -2
2.0000000000
4 3 2 2 -2 2 -2 -2 2 -2
5.0000000000
不公開 測資點#0 (5%): 0.5s , <1K
不公開 測資點#1 (5%): 0.5s , <1K
不公開 測資點#2 (5%): 0.5s , <10M
不公開 測資點#3 (5%): 0.5s , <10M
不公開 測資點#4 (5%): 0.5s , <10M
不公開 測資點#5 (5%): 0.5s , <10M
不公開 測資點#6 (5%): 0.5s , <10M
不公開 測資點#7 (5%): 0.5s , <10M
不公開 測資點#8 (5%): 0.5s , <10M
不公開 測資點#9 (5%): 0.5s , <10M
不公開 測資點#10 (5%): 0.5s , <10M
不公開 測資點#11 (5%): 0.5s , <10M
不公開 測資點#12 (5%): 0.5s , <10M
不公開 測資點#13 (5%): 0.5s , <10M
不公開 測資點#14 (5%): 0.5s , <10M
不公開 測資點#15 (5%): 0.5s , <10M
不公開 測資點#16 (5%): 0.5s , <10M
不公開 測資點#17 (5%): 0.5s , <10M
不公開 測資點#18 (5%): 0.5s , <10M
不公開 測資點#19 (5%): 0.5s , <10M
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