Problem1966--Uniformly Branched Trees

1966: Uniformly Branched Trees

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 (pu,pv) 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.

Input

The single line of the input contains three integers n, d andmod (1≤n≤1000, 2≤d≤10, 108≤mod≤109) − the number of vertices in the tree, the degree of internal vertices and the prime modulo.

Output

Print the number of trees over the modulo mod.

Examples
Input
5 2 433416647
Output
1
Input
10 3 409693891
Output
2
Input
65 4 177545087
Output
910726

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