You are given a directed graph with n vertices and m edges.
How many possible paths start from vertex 1 and end at vertex n?
The given graph is guaranteed to be acyclic (i.e., it has no cycles).
The first input line has two integers n and m: the number of vertices and edges. The vertices are numbered 1, 2, ..., n.
After this, there are m lines describing the edges. Each line has two integers a and b: there is a edge from vertex a to vertex b.
Print one integer: the number of paths from vertex 1 to vertex n.
Since the result may be large, print it modulo 10⁹ + 7.