Baltic Olympiad in Informatics: 2012 Day 1, Problem 2

The well-known mobile network operator Totalphone has set up a number of new base transceiver stations in order to cover a newly-built highway with its network. As always the programmers of Totalphone have been sloppy; as a result, the transmission power cannot be set up individually for the stations, but one can only set the transmission power to a fixed common value for all the stations. In order to minimize power consumption, the company wants to know the maximal distance of a point on the highway to the nearest base transceiver station.

Constraints

$1\le N\le {10}^6$

$1\le L\le {10}^9$

$|x_i|,|y_i|\le {10}^9$

Subtask 1 [25%]

$1\le N\le 5000$

Subtask 2 [25%]

$1\le N\le {10}^5$

Subtask 3 [50%]

No additional constraints.

Input Specification

The first line of input contains two space-separated integers $N$ and $L$ representing the number of base transceiver stations and the length of the highway, respectively.

$N$ lines follow, each containing a pair of integers $x_i$ and $y_i$, which describes the coordinates of a base transceiver station. All points are distinct. Coordinates are sorted in the non-decreasing order with respect to $x_i$ coordinates. If two values of $x_i$ are the same, then coordinates are sorted with respect to $y_i$ coordinates in increasing order.

The highway is a straight line ranging from $(0,0)$ to $(L,0)$.

Output Specification

The only line of output should contain a single number - the maximal distance of a point on the highway to the nearest base transceiver station. Your output will be regarded as correct if it is within an absolute error of ${10}^{-3}$ of the correct answer.

Sample Input

2 10
0 0
11 1

Sample Output

5.545455