It's almost the king's birthday! However, Sammy forgot the exact date. Then Sammy made the mistake of asking Jester for the date. This is what Jester said.

"What, you want to know when is his majesty's birthday? Since you asked me, here is a riddle. 'The day after tomorrow, he turn 32, but he was still 29 on New Year's Day last year. When is his birthday?'"

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Notes! They use the same calendar we use. Bonus riddle; On what day did Sammy ask this question? Answers for both should be in mm/dd format.