My birthday Puzzle, part 1

\[508 \times \overline{SAY} = \overline{HAPPY} + \overline{BIRTH} +\overline{DAY} \]

Each letter represents a different digit from 0 to 9. There are two solutions to this puzzle. State the smaller 9-digit number \(\overline{BIRTHDAYS}\).


You may continue to next puzzle here.
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