158. Commuter Train

time limit per test: 0.5 sec.
memory limit per test: 65536 KB
input: standard input
output: standard output

You might have noticed that bus drivers sometimes pass by passengers waiting for the bus and stop at a place where the distance from the people to the bus doors is maximal. We don't know exact reasons of such behaviour, probably, this is done not because of some special wickedness of the driver but in order to allow passengers in the vehicle to get oR quicker. However, we know that in one country the government decided to implement automatic driving system on their commuter railroads. Among other features, this system is intended to automatically stop commuter trains at stations. A computer in the train is connected to a special radar, which determines passenger positions at the station platform. The computer decides where to stop the train in order to maximize the sum of the distances from each passenger to the closest door. All the hardware is ready, but the software project is late (transport problems). Your task is to implement this function for this software project.
More precisely, the station platform has length 0 < L <= 5000. There are 0 < M <= 300 passengers at the platform. Each passenger p has position Pp (0 <= P1 <= ... <= PM <= L) - the distance from the platform beginning to the passenger. There are 0 < N <= 300 doors in the train. Each door d has position Dd (0 = D1 < D2 < ... < DN <= L) - the distance from it to the door 1. The door width and the passenger sizes are not taken into account. For simplicity assume that the distance between a passenger i and a train door j is dist(i, j, S) = |Dj + S - Pi|, where S is train position - the distance between the first door and the beginning of the platform. Remember that the train must stop so that no door is outside of the platform.

The file contains integer numbers separated by spaces and/or line feeds. At the beginning of the file there is the station description (L, M, and P1 ... PM), followed by the train description (N and D2 ... DN).

You should output two numbers - the train position S, at which the maximal possible sum of the minimal distances between the passengers and the doors can be achieved and the sum itself. If there are many such train positions - output any one.

Sample test(s)

Sample input #1
0 4

Sample input #2
0 1 2 3 4
1 2 3

Sample output #1
2 4

Sample output #2
0.5 2.5


Author:Andrew Lopatin, Nikolay Durov
Resource:ACM ICPC 2002-2003 NEERC, Northern Subregion
Date:November, 2002