{"problem":{"name":"Critical Hit","description":{"content":"There is a monster with initial stamina $N$.   Takahashi repeatedly attacks the monster while the monster's stamina remains $1$ or greater. An attack by Takahashi reduces the monster's stamina by $2$ ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc280_e"},"statements":[{"statement_type":"Markdown","content":"There is a monster with initial stamina $N$.  \nTakahashi repeatedly attacks the monster while the monster's stamina remains $1$ or greater.\nAn attack by Takahashi reduces the monster's stamina by $2$ with probability $\\frac{P}{100}$ and by $1$ with probability $1-\\frac{P}{100}$.\nFind the expected value, modulo $998244353$ (see Notes), of the number of attacks before the monster's stamina becomes $0$ or less.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2\\times 10^5$\n*   $0 \\leq P \\leq 100$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $P$\n\n[samples]\n\n## Notes\n\nWe can prove that the sought expected value is always a finite rational number. Moreover, under the Constraints of this problem, when the value is represented as $\\frac{P}{Q}$ by two coprime integers $P$ and $Q$, we can show that there exists a unique integer $R$ such that $R \\times Q \\equiv P\\pmod{998244353}$ and $0 \\leq R \\lt 998244353$. Print such $R$.","is_translate":false,"language":"English"}],"meta":{"iden":"abc280_e","tags":[],"sample_group":[["3 10","229596204\n\nAn attack by Takahashi reduces the monster's stamina by $2$ with probability $\\frac{10}{100}=\\frac{1}{10}$ and by $1$ with probability $\\frac{100-10}{100}=\\frac{9}{10}$.\n\n*   The monster's initial stamina is $3$.\n*   After the first attack, the monster's stamina is $2$ with probability $\\frac{9}{10}$ and $1$ with probability $\\frac{1}{10}$.\n*   After the second attack, the monster's stamina is $1$ with probability $\\frac{81}{100}$, $0$ with probability $\\frac{18}{100}$, and $-1$ with probability $\\frac{1}{100}$. With probability $\\frac{18}{100}+\\frac{1}{100}=\\frac{19}{100}$, the stamina becomes $0$ or less, and Takahashi stops attacking after two attacks.\n*   If the stamina remains $1$ after two attacks, the monster's stamina always becomes $0$ or less by the third attack, so he stops attacking after three attacks.\n\nTherefore, the expected value is $2\\times \\frac{19}{100}+3\\times\\left(1-\\frac{19}{100}\\right)=\\frac{281}{100}$. Since $229596204 \\times 100 \\equiv 281\\pmod{998244353}$, print $229596204$."],["5 100","3\n\nTakahashi's attack always reduces the monster's stamina by $2$. After the second attack, the stamina remains $5-2\\times 2=1$, so the third one is required."],["280 59","567484387"]],"created_at":"2026-03-03 11:01:14"}}