SIMON-MARAIS 2022 B3

Ari and Sam are playing a game in which they take turns breaking a block of chocolate in two and eating one of the pieces. At each stage of the game the block of chocolate is a rectangle with integer side lengths. On each player’s turn, they break the block of chocolate into two such rectangles along a horizontal or vertical line, and eat the piece with smaller area. (If the two pieces have the same area they may eat either one.) The game ends when the block of chocolate is a $1 \times 1$ rectangle, and the winner is the last player to take their turn breaking the chocolate in two.

At the start of the game the block of chocolate is a $58 \times 2022$ rectangle. If Ari goes first, which player has a winning strategy?