Yet Another Shortest Path Problem

You are given a directed weighted graph with $P$ vertices, labelled from $0$ to $P-1$. $P$ is a prime number. You are also given an integer $K$. For each vertex $u$, there is an edge from vertex $u$ to vertex $(K \cdot u + i) \bmod P$ for all $0 \leq i \leq K-1$. The weight of an edge directed from the vertex $u$ to the vertex $(K \cdot u + i) \bmod P$ is equal to $i$. You will be given $Q$ q