Score : 1200 points

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}.

Constraints

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

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.

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