Both are correct. 'I' can never be used in the objective case, and 'me' can never be used in the subjective case. The subjective case 'I' also appears as a subject complement with linking verbs-- 'It is I' (as does 'me', informally-- 'it is me'); and as a stranded subject-- 'Karen is better at golf than I' (as does 'me', informally-- 'she is better at golf than me').
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