CF382E.Ksenia and Combinatorics

Ksenia has her winter exams. Today she is learning combinatorics. Here's one of the problems she needs to learn to solve.

How many distinct trees are there consisting of n vertices, each with the following properties:

• the tree is marked, that is, the vertices of the tree are numbered from 1 to n;
• each vertex of the tree is connected with at most three other vertices, and at the same moment the vertex with number 1 is connected with at most two other vertices;
• the size of the tree's maximum matching equals k.

Two trees are considered distinct if there are such two vertices u and v, that in one tree they are connected by an edge and in the other tree they are not.

Help Ksenia solve the problem for the given n and k. As the answer to the problem can be very huge you should output it modulo 1000000007 (109 + 7).

克谢尼娅正在准备她的冬季考试。今天她正在学习组合数学。以下是她需要掌握求解的问题之一：

有多少棵互不相同的树，满足以下条件，且该树恰有 $n$ 个顶点：

• 该树是带标号的，即树的顶点编号为 $1$ 到 $n$；
• 树中每个顶点的度数至多为 $3$，且编号为 $1$ 的顶点的度数至多为 $2$；
• 该树的最大匹配的大小恰好为 $k$。

若存在两个顶点 $u$ 和 $v$，使得在其中一棵树中 $u$ 与 $v$ 相邻，而在另一棵树中 $u$ 与 $v$ 不相邻，则称这两棵树互不相同。

请帮助克谢尼娅求出给定 $n$ 和 $k$ 时该问题的答案。由于答案可能非常大，你只需输出其对 $1000000007$（即 $10^9 + 7$）取模的结果。

The first line contains two integers n, k (1 ≤ n, k ≤ 50).

第一行包含两个整数 $n$ 和 $k$（$1 \leq n, k \leq 50$）。

Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

输出一个整数——该问题答案对 $1000000007$（即 $10^9 + 7$）取模的结果。

If you aren't familiar with matchings, please, read the following link: http://en.wikipedia.org/wiki/Matching_(graph_theory).

如果你不熟悉匹配（matching），请阅读以下链接：http://en.wikipedia.org/wiki/Matching_(graph_theory)。