Evading Robot

You are given a **simple undirected connected graph** with $N$ nodes (numbered $1$ to $N$) and $M$ edges. Chef is initially located at vertex $S$, and a robot is located at vertex $A_0 (A_0 \ne S)$. The robot is programmed to move along a specific path, while Chef is trying to avoid meeting with the robot. There is a period of $K$ days, and the robot is programmed with a sequence of $K + 1$ inte