{"problem":{"name":"Overlaps","description":{"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 $x$. Snuke will do the operation below $N$ times. *   Choose two real n","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":6000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc137_f"},"statements":[{"statement_type":"Markdown","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 $R$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq K \\leq \\min(N,10^5)$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc137_f","tags":[],"sample_group":[["2 1","332748118\n\nWe are to find the probability that the two stickers do not overlap, which is $1/3$."],["5 3","66549624"],["10000 5000","642557092"]],"created_at":"2026-03-03 11:01:13"}}