# Ball Game v2

Yolanda and Zachary are sitting at a round table with a number of other people (possibly 0). They play a game in which they pass a ball around the table, always to the person to the left. The ball starts with Yolanda, and after 2017 passes, Zachary has the ball. After $$k$$ additional passes, where $$k$$ is some positive integer, Yolanda has the ball again.

For how many integers $$k$$ between 1 and 2017 inclusive is it possible that Yolanda and Zachary are sitting next to each other?

Inspiration.

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