#P1359E. Modular Stability

    ID: 5386 Type: RemoteJudge 2000ms 512MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>combinatoricsmathnumber theory*2000

Modular Stability

No submission language available for this problem.

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

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 $998244353$.

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 $998244353$.

Samples

7 3
16
3 7
0
1337 42
95147305
1 1
1
500000 1
500000