{"raw_statement":[{"iden":"problem statement","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 $998244353$."},{"iden":"constraints","content":"*   $2\\leq A\\leq 10^{12}$\n*   $0\\leq B\\leq 10^{18}$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$A$ $B$"},{"iden":"sample input 1","content":"2 3"},{"iden":"sample output 1","content":"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 $6$."},{"iden":"sample input 2","content":"924 167"},{"iden":"sample output 2","content":"867046524"},{"iden":"sample input 3","content":"167167167167 0"},{"iden":"sample output 3","content":"0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}