
ZOJ Problem Set  2792
Once upon a time, there was a traveler. He plans to travel using stagecoaches (horse wagons). His starting point and destination are fixed, but he cannot determine his route. Your job in this problem is to write a program which determines the route for him. There are several cities in the country, and a road network connecting them. If there is a road between two cities, one can travel by a stagecoach from one of them to the other. A coach ticket is needed for a coach ride. The number of horses is specified in each of the tickets. Of course, with more horses, the coach runs faster. At the starting point, the traveler has a number of coach tickets. By considering these tickets and the information on the road network, you should find the best possible route that takes him to the destination in the shortest time. The usage of coach tickets should be taken into account. The following conditions are assumed.
InputThe input consists of multiple datasets, each in the following format. The last dataset is followed by a line containing five zeros (separated by a space). n m p a b Every input item in a dataset is a nonnegative integer. If a line contains two or more input items, they are separated by a space. n is the number of coach tickets. You can assume that the number of tickets is between 1 and 8. m is the number of cities in the network. You can assume that the number of cities is between 2 and 30. p is the number of roads between cities, which may be zero.a is the city index of the starting city. b is the city index of the destination city. a is not equal to b. You can assume that all city indices in a dataset (including the above two) are between 1 and m. The second line of a dataset gives the details of coach tickets. t_{i} is the number of horses specified in the ith coach ticket (1<=i<=n). You can assume that the number of horses is between 1 and 10. The following p lines give the details of roads between cities. The ith road connects two cities with city indices x_{i} and y_{i}, and has a distance z_{i} (1<=i<=p). You can assume that the distance is between 1 and 100. No two roads connect the same pair of cities. A road never connects a city with itself. Each road can be traveled in both directions. OutputFor each dataset in the input, one line should be output as specified below. An output line should not contain extra characters such as spaces. If the traveler can reach the destination, the time needed for the best route (a route with the shortest time) should be printed. The answer should not have an error greater than 0.001. You may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied. If the traveler cannot reach the destination, the string "Impossible" should be printed. One cannot reach the destination either when there are no routes leading to the destination, or when the number of tickets is not sufficient. Note that the first letter of "Impossible" is in uppercase, while the other letters are in lowercase. Sample Input3 4 3 1 43 1 2 1 2 10 2 3 30 3 4 20 2 4 4 2 1 3 1 2 3 3 1 3 3 4 1 2 4 2 5 2 4 3 4 1 5 5 1 2 10 2 3 10 3 4 10 1 2 0 1 2 1 8 5 10 1 5 2 7 1 8 4 5 6 3 1 2 5 2 3 4 3 4 7 4 5 3 1 3 25 2 4 23 3 5 22 1 4 45 2 5 51 1 5 99 0 0 0 0 0 Sample Output30.0003.667 Impossible Impossible 2.856 Since the number of digits after the decimal point is not specified, the above result is not the only solution. For example, the following result is also acceptable. 30.03.66667 Impossible Impossible 2.85595 Source: Japan Domestic 2005 