$n$ to the $n^{th}$

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?