The bus station in Joseph's town operates randomly.
Before the bus station opens, there are N buses at the station.
The buses are numbered 0 through N-1.
Whenever a bus has to depart the station, one of these buses is chosen at random.
Different buses may be chosen with different probabilities.
More precisely, for each i, the probability that bus i will be chosen is prob[i]/100.
After bus i departs the station, it follows its specific route.
The time the bus needs to complete its route is time[i].
The bus station opens at time 0.
At that time, the first random bus will depart.
During the day, as soon as a bus returns from its route, a new bus is randomly chosen to depart in that same moment.
(The probability distribution is the same for each random choice, and the random choices are mutually independent.
It is possible that the bus chosen to depart will again be the bus that just arrived.)
Joseph just arrived to the bus station.
The current time is s.
He is going to wait for the next bus.
(If there is a bus departing precisely at the time s, Joseph can still catch it.
In this case, his waiting time is zero.)
You are given the ints time and prob, and the int s.
Return Joseph's expected waiting time.