Problem - Game Routes

This problem asks: How many different routes are there from city $1$ to city $n$ in a flight network (DAG)?

The answer can be huge, so return it modulo $10^9 + 7$. A route is a sequence of cities where you can fly from each city to the next. This is a path counting problem on a DAG.

Instead of taking min or max when relaxing edges, you add: dp[v] = dp[v] + dp[u] for each edge $(u, v)$. Each path to $u$ extends to a path to $v$.