Problem - Game Routes

You have a game with $n$ levels and $m$ teleporters. Each teleporter goes from level $a$ to level $b$. You start at level $1$ and want to reach level $n$. How many different routes are there from level $1$ to level $n$?

Print the answer modulo $10^9 + 7$. This is the counting version of the previous problem.

Instead of finding the longest path, you count all paths. The approach is the same: topological sort plus DP.

But instead of taking the max, you sum the ways. Before reading on, think: what would the DP state be?

What's the transition?