No tag edit access

G. Armistice Area Apportionment

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAfter a drawn-out mooclear arms race, Farmer John and the Mischievous Mess Makers have finally agreed to establish peace. They plan to divide the territory of Bovinia with a line passing through at least two of the *n* outposts scattered throughout the land. These outposts, remnants of the conflict, are located at the points (*x*_{1}, *y*_{1}), (*x*_{2}, *y*_{2}), ..., (*x*_{n}, *y*_{n}).

In order to find the optimal dividing line, Farmer John and Elsie have plotted a map of Bovinia on the coordinate plane. Farmer John's farm and the Mischievous Mess Makers' base are located at the points *P* = (*a*, 0) and *Q* = ( - *a*, 0), respectively. Because they seek a lasting peace, Farmer John and Elsie would like to minimize the maximum difference between the distances from any point on the line to *P* and *Q*.

Formally, define the difference of a line relative to two points *P* and *Q* as the smallest real number *d* so that for all points *X* on line , |*PX* - *QX*| ≤ *d*. (It is guaranteed that *d* exists and is unique.) They wish to find the line passing through two distinct outposts (*x*_{i}, *y*_{i}) and (*x*_{j}, *y*_{j}) such that the difference of relative to *P* and *Q* is minimized.

Input

The first line of the input contains two integers *n* and *a* (2 ≤ *n* ≤ 100 000, 1 ≤ *a* ≤ 10 000) — the number of outposts and the coordinates of the farm and the base, respectively.

The following *n* lines describe the locations of the outposts as pairs of integers (*x*_{i}, *y*_{i}) (|*x*_{i}|, |*y*_{i}| ≤ 10 000). These points are distinct from each other as well as from *P* and *Q*.

Output

Print a single real number—the difference of the optimal dividing line. Your answer will be considered correct if its absolute or relative error does not exceed 10^{ - 6}.

Namely: let's assume that your answer is *a*, and the answer of the jury is *b*. The checker program will consider your answer correct, if .

Examples

Input

2 5

1 0

2 1

Output

7.2111025509

Input

3 6

0 1

2 5

0 -3

Output

0.0000000000

Note

In the first sample case, the only possible line is *y* = *x* - 1. It can be shown that the point *X* which maximizes |*PX* - *QX*| is (13, 12), with , which is .

In the second sample case, if we pick the points (0, 1) and (0, - 3), we get as *x* = 0. Because *PX* = *QX* on this line, the minimum possible difference is 0.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/20/2018 21:16:52 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|