apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.5 seconds
Memory limit: 512.0 MB

# Problem
Alice and Bob are playing yet another card game. This time the rules are the following. There are $$$n$$$ cards lying in a row in front of them. The $$$i$$$-th card has value $$$a_i$$$.

First, Alice chooses a non-empty consecutive segment of cards $$$[l; r]$$$ ($$$l \le r$$$). After that Bob removes a single card $$$j$$$ from that segment $$$(l \le j \le r)$$$. The score of the game is the total value of the remaining cards on the segment $$$(a_l + a_{l + 1} + \dots + a_{j - 1} + a_{j + 1} + \dots + a_{r - 1} + a_r)$$$. In particular, if Alice chooses a segment with just one element, then the score after Bob removes the only card is $$$0$$$.

Alice wants to make the score as big as possible. Bob takes such a card that the score is as small as possible.

What segment should Alice choose so that the score is maximum possible? Output the maximum score.

## Input Format
The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the number of cards.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-30 \le a_i \le 30$$$) — the values on the cards.

## Output Format
Print a single integer — the final score of the game.

## Examples
```input
5
5 -2 10 -1 4
```
```output
6
```
-----
```input
8
5 2 5 3 -30 -30 6 9
```
```output
10
```
-----
```input
3
-10 6 -15
```
```output
0
```

## Note
In the first example Alice chooses a segment $$$[1;5]$$$ — the entire row of cards. Bob removes card $$$3$$$ with the value $$$10$$$ from the segment. Thus, the final score is $$$5 + (-2) + (-1) + 4 = 6$$$.

In the second example Alice chooses a segment $$$[1;4]$$$, so that Bob removes either card $$$1$$$ or $$$3$$$ with the value $$$5$$$, making the answer $$$5 + 2 + 3 = 10$$$.

In the third example Alice can choose any of the segments of length $$$1$$$: $$$[1;1]$$$, $$$[2;2]$$$ or $$$[3;3]$$$. Bob removes the only card, so the score is $$$0$$$. If Alice chooses some other segment then the answer will be less than $$$0$$$.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 512.0 MB

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

## Output Format
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 $$$998244353$$$.

## Examples
```input
7 3
```
```output
16
```
-----
```input
3 7
```
```output
0
```
-----
```input
1337 42
```
```output
95147305
```
-----
```input
1 1
```
```output
1
```
-----
```input
500000 1
```
```output
500000
```

Now solve the problem and return the code.