Q$2.(50$ marks$)$ Write a C$++$ program that asks the user to enter two positive integer numbers as the lower bound and upper bound. Then it asks the user to enter a character: $-$If the entered character is $$a$,$ function$1$ is called. $-$If the entered character is $$b$,$ function$2$ is called and then the value of result variable is printed $-$If the entered character is $$c$,$ function $3$ is called and the returned value of the function $3$ is printed. $-$If the entered character is $$d$,$ function $4$ is called. $-$If the user enters any other character, the program prints $$invalid input$$ and terminates. Function $1$: This function accepts the upper bound and lower bound numbers as the input arguments and prints out all the numbers in this range $($Inclusive$)$ which are multiples of both $3$ and $5.$ Function $2$: This function has no return value. It accepts $3$ input arguments: the upper bound and lower bound numbers and a variable result $($by reference$).$ First, calculating the absolute difference between lower and upper bound numbers, computing the logarithm $($base $10)$ of the absolute difference and save it in the result. $($please note that the number of digits after the decimal point should be set to $4$ for the result value$).$ Function $3$: This function returns a variable of type double $($sum$)$ and accepts the upper bound and lower bound numbers $($lower and upper variables$)$ as input arguments. It calculates the results of following equation and returns the sum variable. $($please note that the number of digits after the decimal point should be set to $3$ for the sum value$).$ sum$=++++...+$ Function $4$: This function has no return value. It accepts the upper bound and lower bound numbers as the input arguments and prints out a Triangle pattern with following rules: $1)$ Get the number of rows for the Triangle: Calculate the sum of lower and upper bound numbers, then take its last digit of the sum. This last digit is the number of rows for the Triangle pattern. $($If the last digit is $0,$ we don$$t print out anything$).2)$ The first and last element of every row is always $1.3)$ The number at position $($n$,$ k$)$ is the binomial coefficient calculated as: T$($n$,$ k$)=$ T$($n$-1,$ k$-1)+$ T$($n$-1,$ k$)$