can i use my xbox controller to play this game or is it mouse + kb only?

I doubt controllers are fully supported. Even though my xbox one controller made the in-game cursor move out-of-the-box, I wasn't able to trigger click events. To be honest, it also doesn't make much sense to use a controller here. The game is clearly made for mouse input. All you do is clicking and drag-and-drop. Both best done with a mouse, as long as there is no dedicated controller input scheme .. and there isn't - the controller is simply emulating the mouse by moving the mouse cursor.