Modular Stability

2000ms

524288K

Description:

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 $$$1 \le a_1 < a_2 < \dots < a_k \le n$$$.

Input:

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

Output:

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 $$$998244353$$$.

Sample Input:

7 3

Sample Output:

Sample Input:

3 7

Sample Output:

Sample Input:

1337 42

Sample Output:

95147305

Sample Input:

1 1

Sample Output:

Sample Input:

500000 1

Sample Output:

Informação

Provedor Codeforces

Código CF1359E