{"problem":{"name":"Access Counter","description":{"content":"Takahashi has decided to put a web counter on his webpage.   The accesses to his webpage are described as follows: *   For $i=0,1,2,\\ldots,23$, there is a possible access at $i$ o'clock every day:   ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc271_g"},"statements":[{"statement_type":"Markdown","content":"Takahashi has decided to put a web counter on his webpage.  \nThe accesses to his webpage are described as follows:\n\n*   For $i=0,1,2,\\ldots,23$, there is a possible access at $i$ o'clock every day:\n    *   If $c_i=$`T`, Takahashi accesses the webpage with a probability of $X$ percent.\n    *   If $c_i=$`A`, Aoki accesses the webpage with a probability of $Y$ percent.\n    *   Whether or not Takahashi or Aoki accesses the webpage is determined independently every time.\n*   There is no other access.\n\nAlso, Takahashi believes it is preferable that the $N$\\-th access since the counter is put is not made by Takahashi himself.\nIf Takahashi puts the counter **right before $0$ o'clock** of one day, find the probability, modulo $998244353$, that the $N$\\-th access is made by Aoki.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{18}$\n*   $1 \\leq X,Y \\leq 99$\n*   $c_i$ is `T` or `A`.\n*   $N$, $X$, and $Y$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $X$ $Y$\n$c_0 c_1 \\ldots c_{23}$\n\n[samples]\n\n## Notes\n\nWe can prove that the sought probability is always a finite rational number. Moreover, under the constraints of this problem, when the value is represented as $\\frac{P}{Q}$ with two coprime integers $P$ and $Q$, we can prove that there is a unique integer $R$ such that $R \\times Q \\equiv P\\pmod{998244353}$ and $0 \\leq R \\lt 998244353$. Find this $R$.","is_translate":false,"language":"English"}],"meta":{"iden":"abc271_g","tags":[],"sample_group":[["1 50 50\nATATATATATATATATATATATAT","665496236\n\nThe $1$\\-st access since Takahashi puts the web counter is made by Aoki with a probability of $\\frac{2}{3}$."],["271 95 1\nTTTTTTTTTTTTTTTTTTTTTTTT","0\n\nThere is no access by Aoki."],["10000000000000000 62 20\nATAATTATATTTAAAATATTATAT","744124544"]],"created_at":"2026-03-03 11:01:13"}}