- Time limit: 1.00 s
- Memory limit: 512 MB
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.
Input
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.
Output
Print the number of paths modulo 10^9+7.
Constraints
- 1 \le n \le 100
- 1 \le m \le n(n-1)
- 1 \le k \le 10^9
- 1 \le a,b \le n
Example
Input:
3 4 8 1 2 2 3 3 1 3 2
Output:
2
Explanation: 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.