P15228 [SWERC 2017] Blowing Candles

As Jacques-Édouard really likes birthday cakes, he celebrates his birthday every hour, instead of every year. His friends ordered him a round cake from a famous pastry shop, and placed candles on its top surface. The number of candles equals the age of Jacques-Édouard in hours. As a result, there is a huge amount of candles burning on the top of the cake. Jacques-Édouard wants to blow all the candles out in one single breath. You can think of the flames of the candles as being points in the same plane, all within a disk of radius $ R $ (in nanometers) centered at the origin. On that same plane, the air blown by Jacques-Édouard follows a trajectory that can be described by a straight strip of width $ W $, which comprises the area between two parallel lines at distance $ W $, the lines themselves being included in that area. What is the minimum width $ W $ such that Jacques-Édouard can blow all the candles out if he chooses the best orientation to blow?

The first line consists of the integers $ N $ and $ R $, separated with a space, where $ N $ is Jacques-Édouard’s age in hours. Then $ N $ lines follow, each of them consisting of the two integer coordinates $ x_i $ and $ y_i $ of the $ i $th candle in nanometers, separated with a space.

Print the value $ W $ as a floating point number. An additive or multiplicative error of $ 10^{-5} $ is tolerated: if $ y $ is the answer, any number either within $ [y - 10^{-5}; y + 10^{-5}] $ or within $ [(1 - 10^{-5})y; (1 + 10^{-5})y] $ is accepted.

#### Limits - $ 3 \leq N \leq 2 \cdot 10^5 $; - $ 10 \leq R \leq 2 \cdot 10^8 $; - for $ 1 \leq i \leq N $, $ x_i^2 + y_i^2 \leq R^2 $; - all points have distinct coordinates.