I asked my old history teacher where the Luftwaffe came from. I mean, the Treaty of Versailles had imposed very strict limits on German air forces and you don't raise an air force overnight.

Know where it came from? Ye Olde Teacher didn't, but I researched it and found out.

The Luftwaffe was trained in...the Soviet Union. Russia. Germany used airfields in Russian to train the pilots who would, in 1940, be flying against Russia.