OIM 2022 Problem 2

Let $S=\{13, 133, \cdots\}$ be the set of the positive integers of the form $133 \cdots 3$ . Consider a horizontal row of $2022$ cells. Ana and Borja play a game: they alternatively write a digit on the leftmost empty cell, starting with Ana. When the row is filled, the digits are read from left to right to obtain a $2022$ -digit number $N$ . Borja wins if $N$ is divisible by a number in $S$ , otherwise Ana wins. Find which player has a winning strategy and describe it.