DK-GEORGMOHR 2025 Problem 3

Alma and Bertha play the following game. Initially they are standing by a blank board. They take turns writing one of the numbers $1$ , $2$ , $...$ , $2025$ on the board. They may not write a number which is already written on the board. Alma begins. One loses the game by being the first to write a number so that $2025$ divides the product of all the numbers on the board. Which player can find a strategy ensuring she will win?