Consider a directed graph that has $n$ nodes and $m$ edges. Your task is to count the number of paths from node $1$ to node $n$ with exactly $k$ edges.
The first input line contains three integers $n$ , $m$ and $k$ : the number of nodes and edges, and the length of the path. The nodes are numbered $1,2,\dots,n$ .
Then, there are $m$ lines describing the edges. Each line contains two integers $a$ and $b$ : there is an edge from node $a$ to node $b$ .
Print the number of paths modulo $10^9+7$ .
3 4 8 1 2 2 3 3 1 3 2· · \n · \n · \n · \n · \n
2\n
The paths are $1 \rightarrow 2 \rightarrow 3 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 1 \rightarrow 2 \rightarrow 3$ and $1 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3$ .