{"problem":{"name":"Multiple Sequences","description":{"content":"Given are integers $N$ and $M$. How many sequences $A$ of $N$ integers satisfy the following conditions? *   $1 \\leq A_i \\leq M \\left(i = 1, 2, \\ldots, N\\right)$ *   $A_{i+1}$ is a multiple of $A_i$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc116_c"},"statements":[{"statement_type":"Markdown","content":"Given are integers $N$ and $M$. How many sequences $A$ of $N$ integers satisfy the following conditions?\n\n*   $1 \\leq A_i \\leq M \\left(i = 1, 2, \\ldots, N\\right)$\n*   $A_{i+1}$ is a multiple of $A_i$. $\\left(i = 1, 2, \\ldots, N - 1\\right)$\n\nSince the answer can be enormous, report it modulo $998244353$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq 2 \\times 10^5$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc116_c","tags":[],"sample_group":[["3 4","13\n\nSome of the sequences $A$ satisfying the conditions follow:\n\n*   $A = \\left(1, 1, 4\\right)$\n*   $A = \\left(3, 3, 3\\right)$\n*   $A = \\left(1, 2, 4\\right)$"],["20 30","71166"],["200000 200000","835917264"]],"created_at":"2026-03-03 11:01:14"}}