Help! I purged every compiz package

I just did something not very clever, I ran by mistake:

sudo apt purge compiz*

But what I really meant to do was:

sudo apt install --reinstall compiz*

Now I don't have a window manager, I can't type anything because my keyboard stopped working and I can only use the mouse.

How can I undo all this mess?

I happen to have a Live USB image in one of my usb flash drives. Can I use it to solve this?

I am running Ubuntu 16.04 LTS Xenial Xerus.

I need help.