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Timus Top Coders: Third Challenge

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J. Empire Strikes Back

Time limit: 1.0 second
Memory limit: 64 MB

Background

Many years have passed since the good and wise emperor George II the Great began to rule the cultural and civilized Empire. Oh, the world he created is so mighty and beautiful! Under his rule majestic cities of marble and steel are being turned into the sky, and huge fields are being scattering with seeds. The children play, the old men laugh, while the workpeople and the peasants forge the common weal...
But once George got to know, that fearful danger threatened the mankind. Malicious and cruel dictator Saddam III the Terrible, who ruled much less cultural and civilized Republic, intends to create the newest chemical weapon and seize the power over the planet.

Problem

According to a secret service report, Saddam constructed N chemical weapon factories within the Republic frontier, which is a circle of radius R with its center at the point (0, 0). Each factory is skillfully disguised as a hospital, a school or an old people's home and located at the point with cartesian coordinates (Xi, Yi).
Saddam's vile intentions did not please George at all. So he decided to destroy all the factories by bombing. All bombs should have the same effective casualty radius and be dropped precisely onto the corresponding factory.
Each bomb transforms any object within its effective casualty radius into a scorching gas cloud. This very fact prompted George to a funny thought, that it would be great to kill two birds with one stone and transform Saddam himself into such cloud. Unfortunately, the secret service failed to define exact whereabouts of the villain. That is why George wants to calculate the effective casualty radius of the bombs so that, being dropped precisely onto the factories, they would destroy Saddam regardless of his location within the Republic. By the way, it needs a lot of very expensive polonium-210 to create a high-power bomb, so the effective casualty radius should be minimal.

Input

The first line contains the integer numbers N (1 ≤ N ≤ 300) and R (1 ≤ R ≤ 1000). Each of the next N lines contains the integer numbers Xi and Yi (Xi2 + Yi2R2) for the corresponding factory.

Output

You should output the desired effective casualty radius. The radius should be printed with at least five digits after decimal point.

Sample

inputoutput
4 4
0 2
0 -2
2 0
-2 0
2.94725152
Problem Author: Nikita Rybak, Ilya Grebnov, Dmitry Kovalioff
Problem Source: Timus Top Coders: Third Challenge
To submit the solution for this problem go to the Problem set: 1520. Empire Strikes Back