Going from unsalted to salted MD5 passwords

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I have a LAMP (PHP) website which is becoming popular.

I played it safe by storing the user passwords as md5 hashes.

But I now see that's not secure; I should have salted the md5 hash - because it's currently possible to decode unsalted md5 hashes using rainbow tables.

What can I do?

I don't want to make everyone type a new password.

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