CSES 1202 Investigation - Problem Statement

You have a directed graph with N cities and M flights. Find these four values for paths starting at city $1$ and ending at city N:

$1.$ Shortest distance.

$2.$ Number of shortest paths (mod $10^9 + 7$).

$3.$ Minimum flights on a shortest path.

$4.$ Maximum flights on a shortest path. Constraints: $N \leq 10^5$, M ≤ $2 \times 10^5$. All four answers come from a single modified Dijkstra run where you maintain extra arrays alongside the distance array.