P9091 "SvR-2" Let's Meet at a Higher Place

$$「Someday, let us meet at a higher place！」$$

Construct an integer sequence $a$ of length $m$ such that for all $1 \leq i \leq m$, $a_i \in [1, n]$. Take its prefix $\gcd$, and record it as an integer sequence $b$. The value $f(n, m, k)$ is the number of **distinct** sequences $b$ that can be constructed in the above way, such that in $b$, the **number of times adjacent terms are equal is $\leq k$**. Given positive integers $n, m$, Little L asks you to compute the value of $\displaystyle\sum_{i = 1}^n \sum_{j = 1}^m \sum_{k = 0}^{j - 1} f(\lfloor \frac{n}{i} \rfloor, j, k)$. Since the result may be very large, you only need to output the value modulo $2^{32}$.

One line with two integers $n, m$.

One line with one integer, representing the required value.

| $\bf{Subtask}$ | $n$ | $m$ | Score | | :------: | :------: | :------: | :------: | | $1$ | $1 \leq n \leq 10^4$ | No special restrictions | $10 \operatorname{pts}$ | | $2$ | $1 \leq n \leq 10^6$ | Same as above | $20 \operatorname{pts}$ | | $3$ | $1 \leq n \leq 10^9$ | Same as above | $20 \operatorname{pts}$ | | $4$ | No special restrictions | $1 \leq m \leq 25$ | $20 \operatorname{pts}$ | | $5$ | Same as above | No special restrictions | $30 \operatorname{pts}$ | For $100\%$ of the testdata, $1 \leq n \leq 10^{10}$ and $1 \leq m \leq 34$. Translated by ChatGPT 5