{"problem":{"name":"Sequence Growing Hard","description":{"content":"Find the number of the possible tuples of sequences $(A_0,A_1,...,A_N)$ that satisfy all of the following conditions, modulo $M$: *   For every $i$ $(0\\leq i\\leq N)$, $A_i$ is a sequence of length $i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc024_e"},"statements":[{"statement_type":"Markdown","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 $A_{i-1}$.\n\n## Constraints\n\n*   $1 \\leq N,K \\leq 300$\n*   $2 \\leq M \\leq 10^9$\n*   $N$, $K$ and $M$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc024_e","tags":[],"sample_group":[["2 2 100","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*   $(),(2),(2,2)$"],["4 3 999999999","358"],["150 150 998244353","186248260"]],"created_at":"2026-03-03 11:01:14"}}