write a C++ program with out using arrays : Consider the following definitions: a. A proper divisors of a positive integer ( 2) is any of its divisors excluding the number itself. For example, the proper divisors of 10 are: 1, 2 and 5. b. A perfect number is a positive integer ( 2) that is equal to the sum of its proper divisors. For example, 6 and 28 are perfect numbers, since: 6 = 1 + 2 + 3 28 = 1 + 2 + 4 + 7 + 14 Background of perfect numbers: https://en.wikipedia.org/wiki/Perfect_number c. Amicable numbers are two different positive integer ( 2), so related that the sum of the proper divisors of each is equal to the other number. For example, 220 and 284 are amicable numbers, since: 284 = 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 220 = 1 + 2 + 4 + 71 + 142 Background of amicable numbers: https://en.wikipedia.org/wiki/Amicable_numbers a. Write a function: void analyzeDividors(int num, int& outCountDivs, int& outSumDivs) The function takes as an input a positive integer num ( 2), and updates two output parameters with the number of num's proper divisors and their sum. For example, if this function is called with num=12, since 1, 2, 3, 4 and 6 are 12s proper divisors, the function would update the output parameters with the numbers 5 and 16. Note: Pay attention to the running time of your function. An efficient implementation would run in . b. Use the function you wrote in section (a), to implement the function: bool isPerfect(int num) This functions is given positive integer num ( 2), and determines if it is perfect number or not. c. Use the functions you implemented in sections (a) and (b), to write a program that reads from the user a positive integer M ( 2), and prints: All the perfect numbers between 2 and M. All pairs of amicable numbers that are between 2 and M (both numbers must be in the range). Note: Pay attention to the running time of your implementation. An efficient algorithm for this part would call analyzeDividors times all together.