Description

Little F is chatting with classmates in math class.

Given a positive integer, compute the number of its divisors.

“You guys in competitions just study this? Too easy.”

“...”

Given a positive integer, compute the sum of the number of divisors of all its divisors.

“Let me think... Hmm, still not hard. Hey, can you still sign up for your competitions?”

“...”

Given a positive integer, compute the sum of the number of divisors of all the divisors of all its divisors.

“Anyway your computers can always brute-force it, right? Hurry up and tell me where to sign up.”

“...”

Given a positive integer, compute the sum of the number of divisors of all the divisors of all the divisors of all its divisors.

“Will this ever end?”

“...”

Mocked, Little F hands this problem to you. Please show your brute-forcing power.

Given a positive integer $N$, compute the sum of divisor counts over the multiset obtained by applying the operation “take all divisors” to $N$ exactly $K$ times.

The answer may be large; output it modulo $998244353$.

Input Format

One line with two integers $N, K(1 \leq N \leq 10 ^ {18}, 0 \leq K \leq 10^{18})$.

Output Format

Output a single non-negative integer: the required answer modulo $998244353$.

4 0

3

4 1

6

4 2

10

Hint

Explanations for Samples 1, 2, 3

$4,\ 0:$ $4$ 的约数 $\ 1\ 2\ 4$

$4,\ 1:$ $4$ 的所有约数的约数 $\ (1)\ (1\ 2)\ (1\ 2\ 4)$

$4,\ 2:$ $4$ 的所有约数的所有约数的约数 $((1))\ ((1)\ (1\ 2))\ ((1)\ (1\ 2)\ (1\ 2\ 4))$

Subtasks

子任务 $1(11 \mathrm{pts}) : N, K \leq 10 ^ 4$

子任务 $2(31 \mathrm{pts}) : N \leq 10 ^ 4$

子任务 $3(41 \mathrm{pts}) : N \leq 10 ^ 9$

子任务 $4(67 \mathrm{pts}) : 1 \leq N \leq 10 ^ {18}, 0 \leq K \leq 10^{18}$。

Translated by ChatGPT 5