QUESTION $1$

Write a C$++$ program with the following specifications:

a$.$ Define a C$++$ function $($name it myfunction$\_$StudentID where StudentID is your actual student ID number$)$ that has two $2$ integer inputs $(N$ and $M)$ and returns a double output $S,$ where

$S={\displaystyle \underset{n=1}{\overset{N}{}}}{\displaystyle \underset{m=1}{\overset{M}{}}}\frac{\sqrt[\phantom{2}]{mn}+e^{\sqrt[\phantom{2}]{m}}+e^{\sqrt[\phantom{2}]{n}}}{mn+2}$

$($Note: in the actual quiz, do not expect a simple sum; practice if$-$else, switch statements, forwhile loops, other mathematical functions such as sin$,$ cos$,$ remainder, exponentiation, etc.$).$

b$.$ In the main function,

i$.$ Read user inputs for $N$ and $M$ from the command window $($console$)$ while ensuring that both $N$ and $M$ are positive $(>0)$ integers. If the user enters non$-$positive numbers, the program should request the user to re$-$enter a positive $)$ number until a valid number is entered.

ii$.$ Use the above function $($myfunction$\_$StudentID$)$ to determine the sum $ for the user inputs $N$ and $M.$ Display the result using $5$ decimal values.

iii. Using the above function and a for loop, display the values of $S$ for $M=10$ and for $N$ values from $1$ to $10(1,2,3,$dots,$10).$ Also, write the resulting values to a file named "doublesum.txt$".$ Display the result using $5$ decimal values in all outputs $($file and command windows$).$