{"problem":{"name":"Ex - Alchemy","description":{"content":"Takahashi has $A$ kinds of level-$1$ gems, and $10^{10^{100}}$ gems of each of those kinds.   For an integer $n$ greater than or equal to $2$, he can put $n$ gems that satisfy all of the following con","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc281_h"},"statements":[{"statement_type":"Markdown","content":"Takahashi has $A$ kinds of level-$1$ gems, and $10^{10^{100}}$ gems of each of those kinds.  \nFor an integer $n$ greater than or equal to $2$, he can put $n$ gems that satisfy all of the following conditions into a cauldron to generate a level-$n$ gem in return.\n\n*   No two gems are of the same kind.\n*   Every gem's level is less than $n$.\n*   For every integer $x$ greater than or equal to $2$, there is at most one level-$x$ gem.\n\nFind the number of kinds of level-$N$ gems that Takahashi can obtain, modulo $998244353$.\nHere, two level-$2$ or higher gems are considered to be of the same kind if and only if they are generated from the same set of gems.\n\n*   Two sets of gems are distinguished if and only if there is a gem in one of those sets such that the other set does not contain a gem of the same kind.\n\nAny level-$1$ gem and any level-$2$ or higher gem are of different kinds.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A \\leq 10^9$\n*   $N$ and $A$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $A$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc281_h","tags":[],"sample_group":[["3 3","10\n\nHere are ten ways to obtain a level-$3$ gem.\n\n*   Put three kinds of level-$1$ gems into the cauldron.\n    *   Takahashi has three kinds of level-$1$ gems, so there is one way to choose three kinds of level-$1$ gems. Thus, he can obtain one kind of level-$3$ gem in this way.\n*   Put one kind of level-$2$ gem and two kinds of level-$1$ gems into the cauldron.\n    *   A level-$2$ gem can be obtained by putting two kinds of level-$1$ gems into the cauldron.\n        *   Takahashi has three kinds of level-$1$ gems, so there are three ways to choose two kinds of level-$1$ gems. Thus, three kinds of level-$2$ gems are available here.\n    *   There are three kinds of level-$2$ gems, and three ways to choose two kinds of level-$1$ gems, so he can obtain $3 \\times 3 = 9$ kinds of level-$3$ gems in this way."],["1 100","100"],["200000 1000000000","797585162"]],"created_at":"2026-03-03 11:01:14"}}