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Contest: Task: Related: TaskE TaskG

Score : $600$ points

Problem Statement

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 $L$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$ $M$ $L$

Output

Print the answer.

Sample Input 1

3 2 3

Sample Output 1

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 $2-3$.

Sample Input 2

4 3 2

Sample Output 2

6

Sample Input 3

300 290 140

Sample Output 3

211917445