It is very hard to wash and especially to dry clothes in winter. But Jane is a very smart girl. She is not
afraid of this boring process. Jane has decided to use a radiator to make drying faster. But the radiator
is small, so it can hold only one thing at a time.

Jane wants to perform drying in the minimal possible time. She asked you to write a program that will
calculate the minimal time for a given set of clothes.

There are n clothes Jane has just washed. Each of them took ai water during washing. Every minute the
amount of water contained in each thing decreases by one (of course, only if the thing is not completely
dry yet). When amount of water contained becomes zero the cloth becomes dry and is ready to be
packed.

Every minute Jane can select one thing to dry on the radiator. The radiator is very hot, so the amount
of water in this thing decreases by k this minute (but not less than zero — if the thing contains less than
k water, the resulting amount of water will be zero).

The task is to minimize the total time of drying by means of using the radiator effectively. The drying
process ends when all the clothes are dry.