The Journey of Nils with Wild Geese

When Nils traveled with the wild geese, his flock flew over a series of lakes. They decided to take a break, and the geese began landing on the lakes. On the first lake, half of the entire flock plus half a goose landed. On the second lake, half of the remaining flock plus half a goose landed. This pattern continued until all the geese had settled on $K$ lakes.

Now, Nils wants to determine how many geese were in the flock initially. Can you help him figure it out?