Problem Description

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?

Input Format

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.

Output Format

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.

3 10
0 0
10 0
0 10

7.0710678118654755

Hint

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.