Good arrays

Time limit2sMemory limit1024 MB

Summary

Count arrays of length n with values up to c where each element is divisible by the next one, modulo 998244353.

Level: Medium6 of 10
Topics: Number theory, Combinatorics, Math
Solved: No attempts yet

Problem

Recently Vasya learned about integer division. Inspired by this sacred knowledge, he decided to learn more about arrays of positive integers that satisfy some divisibility conditions. More precisely, Vasya calls an array $a=\{a_1,a_2,\ldots,a_n\}$ good if for every $i$ from $1$ to $n-1$ , $a_i$ is divisible by $a_{i+1}$ . Count the number of good arrays of length $n$ consisting of integers not greater than $c$ .

Input

The only input line contains two integers $n$ and $c$ ( $1 \le n, c \le 5 \cdot 10^7$ ), the length of the array and the maximum allowed value.

Output

Output a single integer, the total number of good arrays of length $n$ consisting of positive integers not greater than $c$ . Since this number might be large, output its remainder modulo $998\,244\,353$ .

Examples2

Example 1
Input
```
3 3
```
Expected output
```
7
```
Example 2
Input
```
2 6
```
Expected output
```
14
```