Problem - Distinct Routes - Read Statement

Read the problem at https://cses.fi/problemset/task/1711. You have a directed graph with $n$ vertices and $m$ edges. Find the maximum number of edge-disjoint paths from vertex $1$ to vertex $n$. Two paths are edge-disjoint if they do not share any edges (they can share vertices). Output the number of such paths and list each path as a sequence of vertices.

This translates to max flow where each edge has capacity $1$. The flow value is the number of disjoint paths. Then you decompose the flow to extract the actual paths.