{"raw_statement":[{"iden":"problem statement","content":"Find the number of the possible tuples of sequences $(A_0,A_1,...,A_N)$ that satisfy all of the following conditions, modulo $M$:\n\n*   For every $i$ $(0\\leq i\\leq N)$, $A_i$ is a sequence of length $i$ consisting of integers between $1$ and $K$ (inclusive);\n*   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 $A_{i-1}$;\n*   For every $i$ $(1\\leq i\\leq N)$, $A_i$ is lexicographically larger than $A_{i-1}$."},{"iden":"constraints","content":"*   $1 \\leq N,K \\leq 300$\n*   $2 \\leq M \\leq 10^9$\n*   $N$, $K$ and $M$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$ $M$"},{"iden":"sample input 1","content":"2 2 100"},{"iden":"sample output 1","content":"5\n\nFive tuples below satisfy the conditions:\n\n*   $(),(1),(1,1)$\n*   $(),(1),(1,2)$\n*   $(),(1),(2,1)$\n*   $(),(2),(2,1)$\n*   $(),(2),(2,2)$"},{"iden":"sample input 2","content":"4 3 999999999"},{"iden":"sample output 2","content":"358"},{"iden":"sample input 3","content":"150 150 998244353"},{"iden":"sample output 3","content":"186248260"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}