Graph Paths I

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.