A parking garage has N parking spaces, numbered from 1 to N inclusive. The garage opens
empty each morning and operates in the following way throughout the day. Whenever a car
arrives at the garage, the attendants check whether there are any parking spaces available. If
there are none, then the car waits at the entrance until a parking space is released. If a parking
space is available, or as soon as one becomes available, the car is parked in the available
parking space. If there is more than one available parking space, the car will be parked at the
space with the smallest number. If more cars arrive while some car is waiting, they all line up in a
queue at the entrance, in the order in which they arrived. Then, when a parking space becomes
available, the first car in the queue (i.e., the one that arrived the earliest) is parked there.
The cost of parking in dollars is the weight of the car in kilograms multiplied by the specific rate
of its parking space. The cost does not depend on how long a car stays in the garage.
The garage operator knows that today there will be M cars coming and he knows the order of
their arrivals and departures. Help him calculate how many dollars his revenue is going to be
today.
Task
Write a program that, given the specific rates of the parking spaces, the weights of the cars and
the order in which the cars arrive and depart, determines the total revenue of the garage in
dollars.
Constraints
| 1 ≤ N ≤ 100 | The number of parking spaces |
| 1 ≤ M ≤ 2,000 | The number of cars |
| 1 ≤ Rs ≤ 100 | The rate of parking space s in dollars per kilogram |
| 1 ≤ Wk ≤ 10,000 | The weight of car k in kilograms |
Input
Your program must read from standard input the following data:
- The first line contains the integers N and M, separated by a space.
- The next N lines describe the rates of the parking spaces. The sth of these lines contains a
single integer Rs, the rate of parking space number s in dollars per kilogram.
- The next M lines describe the weights of the cars. The cars are numbered from 1 to M
inclusive in no particular order. The kth of these M lines contains a single integer Wk, the
weight of car k in kilograms.
- The next 2*M lines describe the arrivals and departures of all cars in chronological order. A
positive integer i indicates that car number i arrives at the garage. A negative integer -i
indicates that car number i departs from the garage. No car will depart from the garage
before it has arrived, and all cars from 1 to M inclusive will appear exactly twice in this
sequence, once arriving and once departing. Moreover, no car will depart from the garage
before it has parked (i.e., no car will leave while waiting on the queue).
Output
Your program must write to standard output a single line containing a single integer: the total
number of dollars that will be earned by the garage operator today.
Grading
For a number of tests worth 40 points there will always be at least one available parking space
for every arriving car. In these cases no car will ever have to wait for a space.
Sample Input 1
3 4
2
3
5
200
100
300
800
3
2
-3
1
4
-4
-2
-1
Sample Output 1
5300
Explanation for Sample Output 1
Car number 3 goes to space number 1 and pays 300 * 2 = 600 dollars.
Car number 2 goes to space number 2 and pays 100 * 3 = 300 dollars.
Car number 1 goes to space number 1 (which was released by car number 3) and pays 200 * 2
= 400 dollars.
Car number 4 goes to space number 3 (the last remaining) and pays 800 * 5 = 4,000 dollars.
Sample Input 2
2 4
5
2
100
500
1000
2000
3
1
2
4
-1
-3
-2
-4
Sample Output 2
16200
Explanation for Sample Output 2
Car number 3 goes to space number 1 and pays 1,000 * 5 = 5,000 dollars.
Car number 1 goes to space number 2 and pays 100 * 2 = 200 dollars.
Car number 2 arrives and has to wait at the entrance.
Car number 4 arrives and has to wait at the entrance behind car number 2.
When car number 1 releases its parking space, car number 2 parks there and pays 500 * 2 =
1,000 dollars.
When car number 3 releases its parking space, car number 4 parks there and pays 2,000 * 5 =
10,000 dollars.