Navigation drawer and hardware back button: when on root level, exit app or go back?

I have an Android app with several different categories that the user can navigate between using navigation drawer. These categories have drill down views that replace the hamburger icon with a software back button.

What if the user open the app, opens the navigation drawer, selects another category, then presses the hardware back button? Since the app is at root level, should I exit the App? Or should the user be redirected back to the home page?

Different Android apps behave differently. For example GMail and Google Play redirect to previously navigated page. Google Maps and Reddit Sync exit the app.

Which behavior makes the most sense?