I’m working on a python question and need an explanation and answer to help me learn.

don’t have much time to fill it here Write a program for addition, multiplication and division with the remainder of sparse polynomials, i.e. polynomials for which we store only non-zero terms.

A sparse polynomial is specified as a sequence of pairs (e,x), where e is the exponent and x the corresponding coefficient. Pairs are listed in order of decreasing exponents, each on a separate line. The entire polynomial is terminated by the line -1 -1. We never list pairs with zero coefficients, especially the zero polynomial is represented by the line -1 -1 itself.

For example, we write the polynomial 3x?5?x?2+7 as follows:

5 3

2 -1

0 7

-1 -1

The first line of input tells us what operation to perform: add for addition, mul for multiplication, or div for division with a remainder. Two sparse polynomials are entered on the next lines.

Write the result of the operation again in the form of a sparse polynomial. The result of the div operation is two polynomials: the quotient and the remainder after division. Note that the division may result in odd numbers; list them as fractions (we recommend using the Fraction type for calculations).

For example: I need to work this for general input !!

for input

add

6 1

4 3

3 -3

0 5

-1 -1

3 3

0 -3

-1 -1 

is the correct output