I'm given a graph and two weight functions, $w_1$ and $w_2$, such that there doesn't exist a negative loop in the graph in $w_1$ and $w_2$. I'm also given two vertices, $s$ and $t$, and am asked to find the lightest path from $s$ to $t$ in relation to $w_1$, out of all the lightest paths from $s$ to $t$ in relation to $w_2$.
I get that this question begs for me to modify Dijkstra somehow, but I just can't seem to find the intuition to do so. Any guidance would be appreciated!