Oh no! Shorty is having his Basic Calculus Exam today, and he has not studied a single bit. Also, because of his poor results this year, if he fails this exam, he will be expelled!
However, being lazy, he still does not want to study. Instead, he wants you to write a program to answer the exam questions for him.
Each of his exam questions are as follows: Shorty is given a function f (x), and he must find the derivative of that function f '(x), in descending order of the exponents, fully expanded and simplified. There will always be a space between a sign (+/-) and x or any digit.
However, there is one problem. His teacher, Mr Bob, is extremely forgetful and often displays the function incorrectly. Also, he is too lazy to re-write the function. Thus, at times he may ask the class to add or subtract a term from f (x) and re-differentiate it.
At any point in time, Shorty may perform 2 actions:
1: Differentiate the function and output the derivative f '(x).
2: Add a term to f (x).
It is guaranteed that the function given is valid, fully expanded and simplified, and has at most one term for any power of x. The coefficient and exponent of each term will fit into a 32-bit signed integer.
The first line of the input contains the polynomial function f (x).
Each subsequent line will begin with an integer k representing the action Shorty must perform. When k = 2, it will be followed by the term to be added (refer to sample input).
The input will be terminated by a null action k = 0.
Output a line containing the function f '(x), for each time Shorty performs action 1.
Subtask 1 (5%): deg(f (x)) < 2. Mr Bob will never add new terms :)
Subtask 2 (13%): The original function will only contain 1 term. There will be at most 1000 actions performed.
Subtask 3 (82%): No restrictions
Subtask 4 (0%): Sample testcase
x^2 - 2x + 1
2x - 2
2x + 1