Concatenation sum

Logic Level 3

The number 123456789 is concatenated 1729 times to form a certain number:

$A = \underbrace{\overline{123456789123456789\dots 123456789}}_{\text{1729 } (123456789)\text{'s}}$

Similarly, the number 987654321 is concatenated 1729 times to form another certain number:

$B=\underbrace{\overline{987654321987654321\dots 987654321}}_{\text{1729 } (987654321)\text{'s}}$

If $A+B = C$ , find the sum of digits of $C$ .

Bonus: Generalize this.

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