Jana came up with a 2022-digit number and whispered its digit sum to Petr. Petr calculated the digit sum of the number Jana told him and whispered the result to Zuzka. Zuzka also calculated the digit sum of the number she received from Petr and whispered the result, which was a two-digit number, to Adam. Adam did the same with the number from Zuzka, and the digit sum he got was 1.

Which numbers could Petr have whispered to Zuzka? Determine all possibilities.

(I. Jančigová)

Hint. What is the largest possible digit sum of a 2022-digit number?
The digit sum of a 2022-digit number can be at most $2022 \cdot 9=18198$ (i.e., for a number consisting entirely of nines). This is also the largest number that Jana could have whispered to Petr.

The digit sum of a number that is less than or equal to 18198 can be at most 36 (for the number 9999). This is also the largest number that Petr could have whispered to Zuzka.

However, Zuzka whispered a two-digit number with a digit sum of 1 to Adam, i.e., only the number 10. Therefore, Petr whispered a number to Zuzka that is less than or equal to 36 with a digit sum of 10, i.e., either 19 or 28.

Note. The digit sums can be any within the given ranges, so there certainly exist 2022-digit numbers that satisfy all the given information. For example, a number consisting of one 1, 22 nines, and the rest zeros has a digit sum of $1+22 \cdot 9=199$, which has a digit sum of 19, etc.