Contest Duration: - (local time) (120 minutes) Back to Home
C - Multiple Sequences /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 1 \leq A_i \leq M \left(i = 1, 2, \ldots, N\right)
• A_{i+1}A_i の倍数 \left(i = 1, 2, \ldots, N - 1\right)

ただし、答えは非常に大きくなる場合があるので、 998244353 で割った余りを答えてください。

### 制約

• 入力は全て整数
• 1 \leq N \leq 2 \times 10^5
• 1 \leq M \leq 2 \times 10^5

### 入力

N M


### 入力例 1

3 4


### 出力例 1

13


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

### 入力例 2

20 30


### 出力例 2

71166


### 入力例 3

200000 200000


### 出力例 3

835917264


Score : 500 points

### 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


### 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