Looking throw the “Online Judge’s Problem Set Archive” I found a very interesting problem number 498, titled “Polly the Polynomial”. Frankly speaking, I did not solve it, but I derived from it this problem.
Everything in this problem is a derivative of something from 498. In particular, 498 was “... designed to help you remember ... basic algebra skills, make the world a better place, etc., etc.”. This problem is designed to help you remember basic derivation algebra skills, increase the speed in which world becomes a better place, etc., etc.
In 498 you had to evaluate the values of polynomial
a0xn +a1xn−1 +...+an−1x+an.
In this problem you should evaluate its derivative. Remember that derivative is defined as
a0nxn−1 +a1(n−1)xn−2 +...+an−1.
All the input and output data will fit into integer, i.e. its absolute value will be less than 231.
Input
Your program should accept an even number of lines of text. Each pair of lines will represent one problem. The first line will contain one integer - a value for x. The second line will contain a list of integers a0, a1, ..., an−1, an, which represent a set of polynomial coefficients.
Input is terminated by