CF724F Uniformly Branched Trees

A tree is a connected graph without cycles. Two trees, consisting of $ n $ vertices each, are called isomorphic if there exists a permutation $ p:{1,...,n}→{1,...,n} $ such that the edge $ (u,v) $ is present in the first tree if and only if the edge $ (p_{u},p_{v}) $ is present in the second tree. Vertex of the tree is called internal if its degree is greater than or equal to two. Count the number of different non-isomorphic trees, consisting of $ n $ vertices, such that the degree of each internal vertex is exactly $ d $ . Print the answer over the given prime modulo $ mod $ .

The single line of the input contains three integers $ n $ , $ d $ and $ mod $ ( $ 1

Print the number of trees over the modulo $ mod $ .