Ball Sequence

There is an infinite line of people, with person numbered $(i+1)$ standing on the right of person numbered $i$. Chef can do $2$ types of operations to this line of people: - Type $1$: Give a ball to the person number $1$. If there exists a person with two balls, they drop one ball and give the other ball to the person on their right, and this repeats until everyone has at most $1$ ball. - Type