Let \(k=\displaystyle\sum_{n=1}^{10100}{n^n} \pmod{101}\) where \(0\le k\le 100\)

\(k+50\) people sit in a circle. They are numbered \(1\) through \(k+50\). Starting with person \(2\), every other person leaves. So \(2,4,6\) etc leave, and it loops back to the beginning when you get to \(k+50\) because it's a circle. What is the number on the last person to remain after that process?

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