D U PULLOD) (a) Write a python program that (1) asks the user to think of a number from 1 to infinity and (2) then guesses the number using the efficient algorithm described in class (see slide 15 in 3-Recurrences). Assume the user will respond "low", "high", or "correct" after each computer guess. Start your code like this: # Author: # Purpose: guess the user's number print ("Think of a number between 1 and infinity.") guess = 2 nbrGuesses = 1 response=input("Is it " + str (guess)) while response!= "correct": Page 2 of 3 CSC 375 Homework 2 Spring 2020 if response == "low": # TODO: FILL in this part if response == "high": #TODO: FILL in this part print ("Your number is", guess) print ("It took", nbrGuesses, "guesses") (b) This is a bonus question worth up to 5 bonus points! Explain why in worst case your program will need to guess at most o (log2 G) times where G is the user's number being guessed. Hint: How many guesses will be required until the user says "high"? After a "high" response we know the user's number is between Y/2 and Y, where Y is the last guess. How many guesses will binary search require to find the correct