Iterated Divisor Count Sum

Given a positive integer N and a positive integer K, perform K iterations of the following operation:

Define the divisor count function f(x) as the number of positive divisors of x. For the first iteration, we have F₁(N)=f(N). For every subsequent iteration k ≥ 2, we define

$$ F_k(N)=\sum_{d|N} F_{k-1}(d) $$

It can be shown that if the prime factorization of N is given by $$N=\prod_i p_i^{a_i},$$ then the answer can be expressed in closed form as

$$ F_K(N)=\prod_i \binom{a_i+K}{K}, $$

where the binomial coefficient is represented in LaTeX format. Since the answer may be large, output it modulo $$998244353$$.

inputFormat

The input consists of one line containing two space-separated positive integers N and K.

outputFormat

Output a single integer – the value of F_K(N) modulo $$998244353$$.

sample

6 1

4