Problem Statement

Find the number of the possible tuples of sequences (A_0,A_1,...,A_N) that satisfy all of the following conditions, modulo M:

• For every $i (0\leq i\leq N), A_i$ is a sequence of length i consisting of integers between 1 and K (inclusive);
• For every $i (1\leq i\leq N), A_{i-1}$ is a subsequence of A_i, that is$, there exists 1\leq x_i\leq i$ such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};
• For every $i (1\leq i\leq N), A_i$ is lexicographically larger than A_{i-1}.

Input

Input is given from Standard Input in the following format:
N K M

Output

Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.

Constraints

• $1 \leq N,K \leq 300$
• $2 \leq M \leq 10^9$
• N, K and M are integers.

Sample Input 1

2 2 100

Sample Output 1

5

Five tuples below satisfy the conditions:

• (),(1),(1,1)
• (),(1),(1,2)
• (),(1),(2,1)
• (),(2),(2,1)
• (),(2),(2,2)

Sample Input 2

4 3 999999999

Sample Output 2

358

Sample Input 3

150 150 998244353

Sample Output 3

186248260

见题面 Input 部分

见题面 Output 部分