Problem Description

Find the number of undirected graphs with $ N $ vertices that satisfy all of the following conditions, modulo $10^9\ +\ 7$.

• The $ N $ vertices are numbered from $ 1 $ to $ N $.
• The graph has no self-loops or multiple edges (it does not need to be connected).
• If the length of every edge is $ 1 $, the shortest distance between vertices $ 1 $ and $ 2 $ is $ D $.

Input Format

The input is given from the standard input in the following format:

$ N $ $ D $

Output Format

Output the number of graphs that satisfy all the conditions, modulo $10^9\ +\ 7$.

Sample Input and Output

Sample Input #1

4 3

Sample Output #1

2

Sample Input #2

4 2

Sample Output #2

14

Sample Input #3

30 15

Sample Output #3

313862829

Notes/Hints

Notes

Two graphs $ G_1 $ and $ G_2 $ are considered different if and only if:

• There exists an integer pair $ (i, j) $ $(1\ \leq\ i\ <\ j\ \leq\ N)$ such that the edge connecting vertices $ i $ and $ j $ exists in only one of $ G_1 $ or $ G_2 $.

Constraints

• $1\ \leq\ D\ <\ N\ \leq\ 30$
• $ N $ and $ D $ are integers.

Sample Explanation 1

The graphs satisfying the conditions are as follows:

Sample Explanation 3

Please note the modulo $(10^9\ +\ 7)$.

见题面 Input 部分

见题面 Output 部分