A13547 | Modular Stability

We define $x \bmod y$ as the remainder of division of $x$ by $y$ ( $\%$ operator in C++ or Java, mod operator in Pascal).

Let's call an array of positive integers $[a_1, a_2, \dots, a_k]$ stable if for every permutation $p$ of integers from $1$ to $k$ , and for every non-negative integer $x$ , the following condition is met:

$ (((x \bmod a_1) \bmod a_2) \dots \bmod a_{k - 1}) \bmod a_k = (((x \bmod a_{p_1}) \bmod a_{p_2}) \dots \bmod a_{p_{k - 1}}) \bmod a_{p_k} $ That is, for each non-negative integer $x$ , the value of $(((x \bmod a_1) \bmod a_2) \dots \bmod a_{k - 1}) \bmod a_k$ does not change if we reorder the elements of the array $a$ .

For two given integers $n$ and $k$ , calculate the number of stable arrays $[a_1, a_2, \dots, a_k]$ such that $1 \le a_1 < a_2 < \dots < a_k \le n$ .

The only line contains two integers $n$ and $k$ ( $1 \le n, k \le 5 \cdot 10^5$ ).

Print one integer — the number of stable arrays $[a_1, a_2, \dots, a_k]$ such that $1 \le a_1 < a_2 < \dots < a_k \le n$ . Since the answer may be large, print it modulo $998244353$ .