Can't get purchased version of Angry Birds from iCloud to iPhone?

I have an iPad, which has an iCloud email address I created attached to it. I purchased Angry Birds. I now have an iPhone, and created a separate email address for that particular iCloud account. I know that I can add my iCloud address that I have with my iPad, yet I can't seem to get the Angry Birds game that I purchased, even when I sign in to iTunes with my IPad's iCloud account. Is there a way I can get it? Is there something I'm doing wrong, or is it not possible to get my game onto my iPhone (it's the newest iPhone BTW if that matters, and I have an iPad mini)? Thanks in advance!

PS - I have no idea if this is in the right category - hopefully it can be moved if not!)

The reason that you can't use it on your iphone is because they are two different versions. If it says Angry Birds HD then it's only compatible with the iPad, this may be the reason why it may not being shown up on the iphone. I do not know why apple does this but I think apple should be able to let you download the iPad to iPhone, sadly they don't.