magnitude of AIC values?

[jeffmoore]

Given the equation for AIC in MARK:
AIC = -2log(Lik)+2K...

...how is it that AIC takes on the large values it does (often in the hundreds or thousands)?

Assuming natural log is used, I can only get huge AIC values with very tiny likelihoods.
Example: -2*ln(1E-200) = 921
Example: -2*ln(1E-300) = 1382
And I have -2log(lik) values of 3000 for some of my models.

Are max likelihoods are frequently so small as to yield these large AIC values, or is there some constant being attached?

just curious.

thanks,
jeff