# Shortest s-t path when is allowed to ignore k weights

Given an undirected graph $$G$$ with $$n$$ vertices and $$m$$ edges, with non-negative weights on the edges, what's the best algorithm that computes the shortest path from $$s$$ to $$t$$, where you are allowed to ignore the weight (i.e. set to $$0$$) of at most $$k$$ edges on the path?

An $$O(kn\log(kn)+km)$$ homework-level solution will be copy the graph $$k$$ times and use dijkstra. But is there any better algorithm (or lower bound)?