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 5\,000~

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