On a table near the sea, there are $N$ glass boxes where $N<2021$, each containing exactly $2021$ ball, Sowdha and Rafi play a game by taking turns on the boxes where Sowdha takes the first turn, a player selects a non-empty box and throws out some of the balls from it into the sea. If a player wants, he can throw out all of the ball in the selected box. The player who throws out the last ball wins. Let $S$ be the sum of values of $N$ for which Sowdha has a winning strategy, and let $R$ be the sum of values of $N$ for which Rafi has a winning strategy. What is the value of $R-S$?

Combinatorics BdMO

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