Problem Statement

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 $998244353$.

Constraints

• $2\leq A\leq 10^{12}$
• $0\leq B\leq 10^{18}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

A B

Output

Print the answer.