201162: [AtCoder]ARC116 C - Multiple Sequences

Problem Statement

Given are integers $N$ and $M$. How many sequences $A$ of $N$ integers satisfy the following conditions?

• $1 \leq A_i \leq M \left(i = 1, 2, \ldots, N\right)$
• $A_{i+1}$ is a multiple of $A_i$. $\left(i = 1, 2, \ldots, N - 1\right)$

Since the answer can be enormous, report it modulo $998244353$.

Constraints

• All values in input are integers.
• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the answer.

Sample Input 1

3 4

Sample Output 1

13

Some of the sequences $A$ satisfying the conditions follow:

• $A = \left(1, 1, 4\right)$
• $A = \left(3, 3, 3\right)$
• $A = \left(1, 2, 4\right)$

Sample Input 2

20 30

Sample Output 2

71166

Sample Input 3

200000 200000

Sample Output 3

835917264