Problem Statement

You are to generate a graph by the following procedure.

• Choose a simple undirected graph with $N$ unlabeled vertices.
• Write a positive integer at most $K$ in each vertex in the graph. Here, there must not be a positive integer at most $K$ that is not written in any vertex.

Find the number of possible graphs that can be obtained, modulo $P$. ($P$ is a prime.)

Two graphs are considered the same if and only if one can label the vertices in each graph as $v_1, v_2, \\dots, v_N$ to satisfy the following conditions.

• For every $i$ such that $1 \\leq i \\leq N$, the numbers written in vertex $v_i$ in the two graphs are the same.
• For every $i$ and $j$ such that $1 \\leq i \\lt j \\leq N$, there is an edge between $v_i$ and $v_j$ in one of the graphs if and only if there is an edge between $v_i$ and $v_j$ in the other graph.

Constraints

• $1 \\leq K \\leq N \\leq 30$
• $10^8 \\leq P \\leq 10^9$
• $P$ is a prime.
• All values in the input are integers.

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Input

The input is given from Standard Input in the following format:

$N$ $K$ $P$

Output

Print the answer.

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Sample Input 1

3 1 998244353

Sample Output 1

4

The following four graphs satisfy the condition.

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Sample Input 2

3 2 998244353

Sample Output 2

12

The following $12$ graphs satisfy the condition.

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Sample Input 3

5 5 998244353

Sample Output 3

1024

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Sample Input 4

30 15 202300013

Sample Output 4

62712469