P13541 [OOI 2022] Good arrays

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

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

The testset for this problem consists of 7 test groups. You get points for a group only if your solution passes all tests from this group and from all the required groups. $\textbf{Offline-evaluation}$ means that you will not get immediate feedback for this group and you will be able to see the outcome only after the end of the competition. | Group | Points | Additional constraints | < | Required groups | Comment | |:-----:|:------:|:----------------------:|:-:|:---------------:|:-------:| | | | $n$ | $c$ | | | | 0 | $0$ | -- | -- | -- | Sample test cases. | | 1 | $15$ | $n \le 10$ | $c \le 10$ | $0$ | | | 2 | $14$ | $n \le 1000$ | $c \le 1000$ | $0, 1$ | | | 3 | $12$ | $n \le 5000$ | $c \le 5000$ | $0$--$2$ | | | 4 | $16$ | $n \le 100\,000$ | $c \le 100\,000$ | $0$--$3$ | | | 5 | $14$ | $n \le 10^6$ | $c \le 10^6$ | $0$--$4$ | | | 6 | $15$ | $n \le 10^7$ | $c \le 10^7$ | $0$--$5$ | | | 7 | $14$ | -- | -- | $0$--$6$ | **Offline-evaluation.** |