Default [Q] Backup my contact list from a locked Android phone?

My phone is in following condition and I badly need to backup my contact list. Please share a feasible solution

- it is screen locked and is asking for my google credentials because I have entered incorrect pattern multiple times.
- I don't remember the password of my google account
- I don't have USB debugging enabled
- phone model is HTC Desire C
- the phone is in stock condition, hence no recovery is installed

UPDATE: I have researched the available internet and am close to believing that this is not easily possible. However, I cannot settle on the fact that all my data is still intact and it is just a matter of bypassing the screen lock somehow. I hope someone out there might be curious and resourceful enough to achieve what no one has until now. And to repay his/her time and efforts, I offer to design a fully featured website for him/her and waive off 100% of the labor cost incurred (maximum 7 days).