For this assignment you will be required to implement an interactive menu, but first you should welcome the user with a one time only welcome message.

Specific implementation requirements include

This menu will prompt the user to select one of three options.

$1-$ Calculate Greatest Common Denominator

$2-$ Perform Prime Factorization

$3-$ Exit

Your program MUST handle invalid inputs by printing the INVALID$\_$MENU$\_$SELECTION message followed by reprinting the menu.

Once a valid selection is made, your program will print the relevant prompt followed by prompting for the correct number of integers, one line at a time. There will be two prompts for GCD and one for PF$.$

Your program should print the correct solution to the console then go back to the main menu.

If the user enters an invalid input, print the INVALID$\_$INPUT message and return to the main menu. For GCD all integers must be positive. For PF the integer must be $2$ or greater.

For GCD the larger integer could be input either first or last

When the user selects exit, the EXIT$\_$MESSAGE should be printed and the program should end.

The output should match exactly as expected. Use String variables provided in the starter code.

Your program should not crash for any input.

You may not utilize static or multiple Scanner objects.

You may not utilize java.lang.Math for this assignment.

You may not utilize System.exit$()$

write this in java