Options Trading Question

I was explaining option trading to a friend and came up with a question that I don't know the answer to. Perhaps someone out there can help me.

The question concerns how dividends are handled in an option contract. Suppose it is now March and I write a covered call with a May expiration. In April, the stock pays a dividend. In May, the option is in the money and is exercised. Who keeps the dividend? It was paid to me in April, since I held the stock then, but if the option is exercised, do I have to pay the dividend to the new stock owner?

The last covered calls I wrote were for SFI, a dividend paying stock, but no dividends were paid between the time I sold the option and the expiration date, so I did not face this problem. However, if I decide to write some longer term covered calls, this issue will come into play.