Parsing youtube url

I've written a ruby youtube url parser. It's designed to take an input of a youtube url of one of the following structures (these are currently the youtube url structures that I could find, maybe there's more?):

http://youtu.be/sGE4HMvDe-Q
http://www.youtube.com/watch?v=Lp7E973zozc&feature=relmfu
http://www.youtube.com/p/A0C3C1D163BE880A?hl=en_US&fs=1

The aim is to save just the id of the clip or playlist so that it can be embedded, so if it's a clip: 'sGE4HMvDe-Q', or if it's a playlist: 'p/A0C3C1D163BE880A'

The parser I wrote works fine for these urls, but seems a bit brittle and long-winded, I'm just wondering if someone could suggest a nicer ruby approach to this problem?

def parse_youtube
    a = url.split('//').last.split('/')
    b = a.last.split('watch?v=').last.split('?').first.split('&').first
    if a[1] == 'p'
        url = "p/#{b}"
    else
        url = b
    end
end