Google Calendar sync fails after deleting stock calendar app in CM11

I installed CM11 on my Nexus 4. After I installed Google Calendar, I thought deleting stock AOSP calendar app and few other depending apps wont hurt. Unfortunately Google calendar sync stopped working after that. "Calendars to display" was empty and "Calendars to sync" never completed loading. When I searched for solution for this online, people suggested to do a reset; which I didn't want to do. So I tried reinstalling the default AOSP calendar app. It fixed the problem!!!

Download the following apks and install them on your phone.

GoogleCalendarSyncAdapter.apk
SecCalendar.apk
SecCalendarProvider.apk

Update
Some people say that they face the following error while signing in.

"Couldn't sign in. There was a problem communicating with Google servers. Try again later"

After installing the above apks, if you open the calendar app directly you will get this error. You have to restart the phone to fix it.