{"raw_statement":[{"iden":"problem statement","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 $R$."},{"iden":"constraints","content":"*   $1 \\le N,M \\le 2 \\times 10^5$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 3"},{"iden":"sample output 1","content":"499122182\n37\n748683574\n\nFor $i=1$, you should find the expected value of the number of times we roll the die, which is $\\frac{11}{2}$."},{"iden":"sample input 2","content":"7 8"},{"iden":"sample output 2","content":"449209977\n705980975\n631316005\n119321168\n62397541\n596241562\n584585746\n378338599"},{"iden":"sample input 3","content":"2023 7"},{"iden":"sample output 3","content":"442614988\n884066164\n757979000\n548628857\n593993207\n780067557\n524115712"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}