Problem p03904 - Generation 2

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.
A string \(S\) of digits, with length \(|S|\) such that \(0 ≤ |S| ≤ 100,000\).

### 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, I can help you create a test case generator for the described problem. Below is the Python code for the test case generator:

```python
import random

def tcgen():
    # Generate a random length for the string S within the given constraints
    max_length = 100000
    S_length = random.randint(1, max_length)
    
    # Generate a random string S consisting of digits between 1 and 9
    S = ''.join(random.choice('123456789') for _ in range(S_length))
    
    # Generate a random value for K such that 0 ≤ K < |S|
    K = random.randint(0, S_length - 1)
    
    return K, S

# Example of generating a test case and printing it
K, S = tcgen()
print(K)
print(S)
```

### Explanation

1. **String Length (`S_length`)**: The length of the string \(S\) is randomly chosen between 1 and 100,000 (inclusive).
2. **String Generation (`S`)**: A string of length `S_length` is generated, consisting of random digits between 1 and 9.
3. **Commas (`K`)**: A random integer \(K\) is generated such that \(0 \leq K < \text{length of } S\).

### Usage

Run the above script to generate a random test case. The generated test case will consist of an integer \(K\) and a string \(S\) that can be used to test the solution for the problem. Each run of the script will produce different random values for \(K\) and \(S\) within the specified constraints.

### Example Output

Here is an example of what the output might look like when you run the script:

```
5234
827364928364928374928374987234987234987234897234987
```

This output can be used as input for the problem statement.

Extract Arguments

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