I ran model selection by delta AIC but encountered most of the AIC as negative.

(R package AICcmodavg and stat : AIC)

As reviewed by reference,

AIC is defined as

-2*log-likelihood + k*npar,

where npar represents the number of parameters in the fitted model, and k = 2 for the usual AIC, or k = \log(n) (n the number of observations)

I would like to ask under what condition will AIC become negative ?

How to test if my case satisfy the condition?

(Is it possible to have a log-likelihood over 1 ?)

Thank you