Mobile
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.
Input
The first line of input file consists of two integers N (1 ≤ N ≤ 10^6) and L (1 ≤ L ≤ 10^9) representing the number of base transceiver stations and the length of the highway, respectively. N lines follow, each containing a pair of integersx_i, y_i (-10^9 ≤ x_i, y_i ≤ 10^9) 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
The first and only line of output file 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 differs by at most 10^{-3} from the precise result.