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.

Input

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

Output

Print the answer.

Constraints

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

Sample Input 1

2 3

Sample Output 1

6

The 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.

Sample Input 2

924 167

Sample Output 2

867046524

Sample Input 3

167167167167 0

Sample Output 3

0

见题面 Input 部分

见题面 Output 部分