A cloud service provider offers quantity discounts based on the number of virtual machines a customer needs. Their offerings vary from 2 to 2000 instances. When pricing is requested, the customer's representative refers to a list of past pricing. Given a list of past price quotes and the number of instances a customer needs, determine the per-instance price for the customer.

The method for determining price is as follows:

• If the number of instances needed is exactly the same as the quantity for a prior customer, the unit price is that price.
• If there is a price for a larger number and a price for a smaller number of instances, linearly interpolate the price of the quantity needed from the unit prices for the closest smaller and larger quantities.
• If the quantities for which there is past data are all smaller or all larger than the amount needed, then linearly extrapolate the unit price from the 2 points closest to the quantity needed.
• If the database only has 1 quantity, that is the price per unit.
• Sometimes, price quotes lapse. When that happens, the old pricing is overwritten with either a 0 or a negative number. The quantities associated with zero or negative unit prices must be disregarded.