{"problem":{"name":"Product of Divisors","description":{"content":"At most how many times can the product of all positive divisors of $A^{B}$ be divided by $A$? It can be shown from the constraints that this count is finite, so find it modulo $998244353$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc167_b"},"statements":[{"statement_type":"Markdown","content":"At most how many times can the product of all positive divisors of $A^{B}$ be divided by $A$?\nIt can be shown from the constraints that this count is finite, so find it modulo $998244353$.\n\n## Constraints\n\n*   $2\\leq A\\leq 10^{12}$\n*   $0\\leq B\\leq 10^{18}$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$A$ $B$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc167_b","tags":[],"sample_group":[["2 3","6\n\nThe positive divisors of $A^{B}=8$ are $1$, $2$, $4$, and $8$, whose product is $64$. $64$ can be divided by $2$ at most six times, so print $6$."],["924 167","867046524"],["167167167167 0","0"]],"created_at":"2026-03-03 11:01:14"}}