Find the number of graphs with $N$ labeled vertices and $M$ unlabeled edges, not necessarily simple or connected, that satisfy the following conditions, modulo $(10^9+7)$:

-   There is no self-loop;
-   The degree of every vertex is at most $2$;
-   The maximum of the sizes of the connected components is exactly $L$.

Input is given from Standard Input in the following format:

```
$N$ $M$ $L$
```

Print the answer.

-   $2 \leq N \leq 300$
-   $1\leq M \leq N$
-   $1 \leq L \leq N$
-   All values in input are integers.

3

When the vertices are labeled 1 through N, the following three graphs satisfy the condition:

• The graph with edges 1−2 and 2−3;
• The graph with edges 1−2 and 1−3;
• The graph with edges 1−3 and 2−3.