{"problem":{"name":"Dice Game","description":{"content":"We have an $N$\\-sided die where all sides have the same probability to show up. Let us repeat rolling this die until every side has shown up. For integers $i$ such that $1 \\le i \\le M$, find the expec","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":6000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc154_f"},"statements":[{"statement_type":"Markdown","content":"We have an $N$\\-sided die where all sides have the same probability to show up. Let us repeat rolling this die until every side has shown up.\nFor integers $i$ such that $1 \\le i \\le M$, find the expected value, modulo $998244353$, of the $i$\\-th power of the number of times we roll the die.\nDefinition of expected value modulo $998244353$It can be proved that the sought expected values are always rational numbers. Additionally, under the constraints of this problem, when such a value is represented as an irreducible fraction $\\frac{P}{Q}$, it can be proved that $Q \\neq 0 \\pmod{998244353}$. Thus, there is a unique integer $R$ such that $R \\times Q = P \\pmod{998244353}$ and $0 \\le R < 998244353$. Print this $R$.\n\n## Constraints\n\n*   $1 \\le N,M \\le 2 \\times 10^5$\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$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc154_f","tags":[],"sample_group":[["3 3","499122182\n37\n748683574\n\nFor $i=1$, you should find the expected value of the number of times we roll the die, which is $\\frac{11}{2}$."],["7 8","449209977\n705980975\n631316005\n119321168\n62397541\n596241562\n584585746\n378338599"],["2023 7","442614988\n884066164\n757979000\n548628857\n593993207\n780067557\n524115712"]],"created_at":"2026-03-03 11:01:13"}}