VIII Olimpiada Informatyczna 2000/2001

Task: POD

Author: Zbigniew Czech

II stage contest, the second day 
Let' us consider a diagram describing a net of municipal transportation, for example a busnet, tramnet or undergroundnet etc. Vertices of the diagram
(numbered 1,2,...,n), correspond to stations, edges (p_{i},p_{j}),
(were p_{i} <>p_{j}) denote
that there is a direct connections from the station
p_{i} to the station p_{j} (1<=p_{i},
p_{j}<=n). Transportation lines are numbered 1,2,...,k. The transportation line
no. l is defined as a series of stations
p_{l,1}, p_{l,2},...,p_{l,sl}, on which vehicles of the
line no. l stop, and durations r_{l,1}, r_{l,2},...,r_{l,sl1}
of traveling between stations  r_{l,1}
is the time necessary to get from the station
p_{l,1} to the station
p_{l,2}, or vice versa (i.e. from the station
p_{l,2} to the station
p_{l,1});
r_{l,2} is the time necessary to get from the station
p_{l,2} to
p_{l,3}, etc. All the stations of a line are different (i.e. i<>j
implies
p_{l,i}<>p_{l,j}). In the
transportation line no. l vehicles run with certain frequency c_{l}, where
c_{l}
is a number from the set {6, 10, 12, 15, 20, 30, 60}. The vehicles in the
transportation line no. l start from the station
p_{l,1} at each hour of the day and night, g:0, (0<=g<=23), and than according to the frequency of the line i.e. at
g:c_{l},g:2c_{l},... etc. (g:c_{l} means
c_{l} minutes after hour g). Vehicles of the line l
run in two directions: from the station
p_{l,1} to p_{l,sl},
and from the station
p_{l,sl}
to
p_{l,1}. The hours of departure of the vehicles of the
transportation line no. l from the station p_{l,sl}
are the same as from the station
p_{l,1}.
In such a transportation net we want to make a trip from the start station x to the finish station
y. We assume that the trip is possible and will take no longer than 24 hours. During the trip one can change
transportation lines as many times as he/she wants to. Say, the time of a change is equal to 0, however, while changing the line we have
to take under consideration the time of waiting for the vehicle that we want to get into. Our
purpose is to get from the start station x, to the finish station y,
as quick as it is possible.
On the picture below you can see a scheme of the transportation net with 6 stations and two lines: no. 1 and no. 2. Vehicles of the line no. 1 go between stations 1, 3, 4 and 6, vehicles of the line no. 2 go between stations 2, 4, 3 and 5. The frequencies with which the vehicles run are equal to c_{1}=15 and c_{2}=20 respectively. The durations of travel between stations are written next to the edges of the net; they are given indices 1 and 2 for particular lines.
Write a program which:
In the first line of the text file POD.IN there are written six integers, separated by single spaces:
The stations are numbered from 1 to n, the transportation lines from 1 to k. In the following 3k lines the transportation lines are described  the description of each of them takes three consecutive lines.
The total number of stations on all transportation lines is not greater than 4000 (i.e. s_{1}+s_{2}+...+s_{k}<=4000).
Your program should write in the only line of the text file POD.OUT two integers, separated by a single space: the hour of the earliest possible arrival to the finish station g_{y} (0<=g_{y}<=23) and the minute of the earliest possible arrival to the finish station m_{y} (0<=m_{y}<=59).
For the input file POD.IN:
6 2 5 6 23 30 4 15 1 3 4 6 9 12 10 4 20 5 3 4 2 11 17 11the correct answer is the output file POD.OUT:
0 16