CSES - Graph Paths I
  • 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 $1 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 2 \rightarrow 3$.