Game with numbers

Discrete Mathematics Level pending

The numbers \(1,2,3,\dots,99,100\) are written on a blackboard. Carl and David take turns, and Carl goes first. On each turn, one of Carl or David erases a number on the board, and adds it to a separate total. Also, the total must always have a digit sum of 9. Whoever chooses a number so that the total no longer has a digit sum of 9 is the loser.

If both players play optimally, who wins?

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