Design an online shopping cart application for VMart using PHP. The home page should have a form for getting username and password. If the credentials are correct, start a session and forward to a catalogue page. The catalogue page should display the item name, item availability and price along with checkbox and textbox for selecting the items of choice and entering the quantity. The submit button in catalogue page should forward the request to a cart page that displays the list of items purchased and the total cost. Perform session management to provide the user with the option to add, update or remove the purchases from the catalogue which must be reflected in the cart. Provide a sign-out link in cart page that terminates the session.