Problem p03904 - Generation 3

Orig Description

Score : 1000 points
Problem StatementYou are given a string S consisting of digits between 1 and 9, inclusive.
You will insert at most K commas (,) into this string to separate it into multiple numbers.
Your task is to minimize the maximum number among those produced by inserting commas. Find minimum possible such value.
Constraints
0 ≦ K < |S| ≦ 100,000
S consists of digits between 1 and 9, inclusive.
Partial Scores
In the test set worth 100 points, |S| ≦ 2.
In the test set worth another 100 points, |S| ≦ 16.
In the test set worth another 200 points, |S| ≦ 100.
In the test set worth another 200 points, |S| ≦ 2,000.
InputThe input is given from Standard Input in the following format:
K
S
OutputPrint the minimum possible value.
Sample Input 12
15267315
Sample Output 1315
When the string is separated into 152, 67 and 315, the maximum among these is 315, which is the minimum possible value.
Sample Input 20
12456174517653111
Sample Output 212456174517653111
12456174517653111 itself is the answer.
Sample Input 38
127356176351764127645176543176531763517635176531278461856198765816581726586715987216581
Sample Output 35317635176

Extracted Specification

An integer K (0 ≤ K < 100,000), representing some quantity or limit.
A string S consisting of digits between '1' and '9', inclusive, with a length |S| (1 ≤ |S| ≤ 100,000).

### Example Input:

```
2
15267315
```

### Function Signature:
Write a function f(K, S) that takes in the input. 
```python
def f(K: int, S: str):
    ''' 
    K: an integer
    S: a string of digits
    '''
```

Test Case Generator

Sure! Here's a test case generator for the given problem statement:

### Test Case Generator

```python
import random

def generate_test_case():
    # Define the constraints
    MAX_LENGTH = 100000
    S = ''.join(random.choice('123456789') for _ in range(random.randint(1, MAX_LENGTH)))
    K = random.randint(0, len(S) - 1)
    
    return K, S

# Example usage:
if __name__ == "__main__":
    K, S = generate_test_case()
    print(K)
    print(S)
```

### Explanation:
1. **Import the required module**: `random` for generating random numbers.
2. **Define the constraints**:
    - `MAX_LENGTH` is set to 100,000, as per the problem constraints.
3. **Generate the string `S`**:
    - The length of `S` is randomized between 1 and `MAX_LENGTH`.
    - Each character in `S` is randomly chosen from '1' to '9'.
4. **Generate the integer `K`**:
    - `K` is a random integer between 0 and `len(S) - 1`.
5. **Return `K` and `S`**:
    - The function returns the generated values of `K` and `S`.

### Example Execution:
Running the example usage part will generate a random test case and print it. For instance, it might output something like:
```
5
8273649182736
```

This randomization ensures that the test cases cover a wide range of possible inputs within the given constraints.

Extract Arguments

def extract_arguments(fh):
    K = int(fh.readline().strip())
    S = fh.readline().strip()
    return K, S