{"raw_statement":[{"iden":"problem statement","content":"We have a bar of length $1$. A point on the bar whose distance from the left end of the bar is $x$ is said to have a coordinate $x$.\nSnuke will do the operation below $N$ times.\n\n*   Choose two real numbers $x$ and $y$ uniformly at random from $[0, 1]$. Put a sticker covering the range from the coordinate $\\min(x,y)$ to the coordinate $\\max(x,y)$.\n\nHere, all random choices are independent of each other.\nStickers can overlap. The bar is said to be good when no point is covered by $K+1$ or more stickers.\nFind the probability, modulo $998244353$, of having a good bar after putting $N$ stickers.\nDefinition of a probability modulo $998244353$It can be proved that the sought probability is always a rational number. Additionally, under the Constraints of this problem, when that value is represented as an irreducible fraction $\\frac{P}{Q}$, it can be proved that $Q \\not \\equiv 0 \\pmod{998244353}$. Thus, there is a unique integer $R$ such that $R \\times Q \\equiv P \\pmod{998244353}, 0 \\leq R < 998244353$. Report this $R$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq K \\leq \\min(N,10^5)$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"2 1"},{"iden":"sample output 1","content":"332748118\n\nWe are to find the probability that the two stickers do not overlap, which is $1/3$."},{"iden":"sample input 2","content":"5 3"},{"iden":"sample output 2","content":"66549624"},{"iden":"sample input 3","content":"10000 5000"},{"iden":"sample output 3","content":"642557092"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}