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 $*mod*$.

Input

The single line of the input contains three integers $*n*$, $*d*$ and $*mod*$ ($1 ≤ *n* ≤ 1000$, $2 ≤ *d* ≤ 10$, $10^{8} ≤ *mod* ≤ 10^{9}$)  — 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 $*mod*$.