# Trucking

Time Limit: 5 Seconds Memory Limit: 32768 KB

A certain local trucking company would like to transport some goods on a cargo truck from one place to another. It is desirable to transport as much goods as possible each trip. Unfortunately, one cannot always use the roads in the shortest route: some roads may have obstacles (e.g. bridge overpass, tunnels) which limit heights of the goods transported. Therefore, the company would like to transport as much as possible each trip, and then choose the shortest route that can be used to transport that amount.

For the given cargo truck, maximizing the height of the goods transported is equivalent to maximizing the amount of goods transported. For safety reasons, there is a certain height limit for the cargo truck which cannot be exceeded.

## Input

The input consists of a number of cases. Each case starts with
two integers, separated by a space, on a line. These two integers
are the number of cities (`C`) and the number of roads
(`R`). There are at most 1000 cities, numbered from
1. This is followed by `R` lines each containing the city
numbers of the cities connected by that road, the maximum height
allowed on that road, and the length of that road. The maximum
height for each road is a positive integer, except that a height
of -1 indicates that there is no height limit on that road. The
length of each road is a positive integer at most 1000. Every road
can be travelled in both directions, and there is at most one road
connecting each distinct pair of cities. Finally, the last line of
each case consists of the start and end city numbers, as well as
the height limit (a positive integer) of the cargo truck. The
input terminates when `C` = `R` = 0.

## Output

For each case, print the case number followed by the maximum height of the cargo truck allowed and the length of the shortest route. Use the format as shown in the sample output. If it is not possible to reach the end city from the start city, print "cannot reach destination" after the case number. Print a blank line between the output of the cases.

## Sample Input

5 6 1 2 7 5 1 3 4 2 2 4 -1 10 2 5 2 4 3 4 10 1 4 5 8 5 1 5 10 5 6 1 2 7 5 1 3 4 2 2 4 -1 10 2 5 2 4 3 4 10 1 4 5 8 5 1 5 4 3 1 1 2 -1 100 1 3 10 0 0

## Sample Output

Case 1: maximum height = 7 length of shortest route = 20 Case 2: maximum height = 4 length of shortest route = 8 Case 3: cannot reach destinationSubmit

Source: Rocky Mountain 2008