A group of 2017 students \(S_0, S_1, S_2,\ldots, S_{2016}\) sit in this order around a circle, going clockwise.

Starting from student \(S_0\) with the number 1, and going clockwise, they consecutively count the numbers 1, 2, and 3, and repeat.

Each student that counts 2 or 3 as they do this must leave the circle, and they continue until only one student \(S_k\) remains.

Determine \(k\).

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