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.

Input

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

Output

Print the answer.

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.

Sample Input 1

3 1 998244353

Sample Output 1

4

The following four graphs satisfy the condition.

Sample Input 2

3 2 998244353

Sample Output 2

12

The following 12 graphs satisfy the condition.

Sample Input 3

5 5 998244353

Sample Output 3

1024

Sample Input 4

30 15 202300013

Sample Output 4

62712469

见题面 Input 部分

见题面 Output 部分