Problem - Xenia and Ringroad

You're given a ring road with $n$ houses numbered $1$ to $n$ in clockwise order. Xenia starts at house $1$ and needs to visit $m$ specific houses in a particular order. Each move from one house to the next clockwise neighbor takes $1$ minute.

Your task: calculate the minimum time needed to visit all required houses in the given order. This tests your understanding of modular arithmetic and how to handle circular structures with vectors.

Before reading further, think: what happens when you need to go from house $5$ to house $2$ on a ring road with $7$ houses? How many moves does that take?