How to get my Angry Birds progress back?

I recently deleted the angry birds app (and other angry birds games) from my iPhone 4s to make more space available (I was on vacation taking pictures.) I selected the option to keep the info in Game Center so I figured that I would still have my progress when I synced my photos to my computer.

I've cleared up room on my phone and downloaded the apps again via iCloud, but none of my data returned. It's saying I have to start over. Please, please, please, can someone tell me how to get the progress on the apps back?

I already synced to iTunes to get some new music and so far looks like I screwed up everything.

That's easy… Just start at the beginning and eventually you'll work your way back to where you were at originally.

Seems like you should have just deleted music since you already have a back up copy of that on your computer at home.