Problem Description
Everyone knows spanning trees, especially MST problem. But most of them are not familiar with degree constrained spanning tree.
a degree-constrained spanning tree is a spanning tree which the maximum vertex degree is limited to a certain constant d.
Given two integers n and d, your task is to count the number of degree constrained spanning trees of a (labeled) complete graph with n vertices.
Input
Each line contains two integers n, d. 1<=n<=100, 1<=k<=100.
Output
For each query, output a line which contains only one integer, the number of degree constrained spanning trees of a (labeled) complete graph with n vertices. This number may be very large, so output the answer modulo 20090829.
Sample Input
3 1
3 2
4 2
10 3
Sample Output
0
3
12
3458313
