{"raw_statement":[{"iden":"statement","content":"Once upon a time, there was a witch named Geor Autumn, who set off on a journey across the world. Along the way, she would meet all kinds of people, from a country full of ICPC competitors to a horse in love with dota---but with each meeting, Geor would become a small part of their story, and her own world would get a little bit bigger.\n\nGeor just arrived at the state of Shu where people love poems. A poem is a permutation $(a_1,\\ldots, a_n)$ of $[n]$. ($(a_1,\\ldots, a_n)$ is a permutation of $[n]$ means that each $a_i$ is an integer in $[1,n]$ and that $a_1,\\ldots, a_n$ are distinct.) One poem is $\\textit{good}$ if for all integer $i$ satisfying $i> k$ and $i\\le n$, $a_i>\\min(a_{i-k}, \\ldots, a_{i-1})$. Here $\\min(a_{i-k}, \\ldots, a_{i-1})$ denotes the minimum value among $a_{i-k}, \\ldots, a_{i-1}$.\n\nHelp Geor calculate how many good poems there are, given $n$ and $k$. To avoid huge numbers, output the answer modulo $998244353$."},{"iden":"input","content":"The first line contains two integers $n$ and $k$ separated by a single space ($1\\le n\\le 10^7$, $1\\le k\\le 10^7$)."},{"iden":"output","content":"Output only one integer in one line---the number of good poems modulo $998244353$."}],"translated_statement":null,"sample_group":[["1 1","1"],["2 3","2"],["3 2","4"],["4 2","10"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}