Implement a hypothetical file system (using a program level data structure) in C++ that would create a directory of files based on user input. Since you've already worked with binary search trees, you may modify it to implement the hypothetical file system. Than way your file system will also be in some sorted order. Use string.compare() for comparing file names. Your program should be menu driven with the following options:

1. Create new folder- Create the folder based on the specified name input by the user and inserted in the correct position in the binary search tree.

2. View file system -Print all folder names currently in the binary search tree in increasing order with each folder name on a separate line. Subfolders should be displayed using indentation.