Problems with Logitech G402 buttons

I recently bought Logitech G402 and I've got some problems with its customising. I use OS X.

Apple's mouse can, for instance, swipe between full-screens. I want to bind two side buttons for those gestures.

Also I need this buttons for games. The only thing that I can do is to bind a key from the keyboard in the game and bind the same key for the side button. But I hope, that I can make some kind of "free" button which would be perceived by the game. Like in the image (mouse1, mouse 2).