7672: [CSES Problem Set] Graph Paths I
[Creator : ]
Description
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.
Your task is to count the number of paths from node $1$ to node $n$ with exactly $k$ edges.
Input
The first input line contains three integers $n, m, k$: 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 $b$.
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 $b$.
Output
Print the number of paths modulo $10^9+7$.
Constraints
$1≤n≤100$
$1 \le m \le n(n-1)$
$1 \le k \le 10^9$
$1 \le a,b \le n$
$1 \le m \le n(n-1)$
$1 \le k \le 10^9$
$1 \le a,b \le n$
Sample 1 Input
3 4 8
1 2
2 3
3 1
3 2
Sample 1 Output
2
The paths are $1 \rightarrow 2 \rightarrow 3 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 1 \rightarrow 2 \rightarrow 3$ and $1 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3$.