Sure, let's write a test case generator for this problem. The test case generator should create random values for \(N\), \(K\), and the set \(A\) based on the constraints given in the problem statement.

Here is a Python function to generate test cases for the problem:

```python
import random

def tcgen():
    # Generate N in the range [1, 100]
    N = random.randint(1, 100)

    # Generate K in the range [1, 10^5]
    K = random.randint(1, 10**5)
    
    # Generate a sorted list A of size N with unique elements in the range [1, K]
    A = sorted(random.sample(range(1, K + 1), N))
    
    return N, K, A

# Function to format the test case as input
def format_test_case(N, K, A):
    return f"{N} {K}\n" + " ".join(map(str, A))

# Generate a test case
N, K, A = tcgen()

# Print the formatted test case
print(format_test_case(N, K, A))
```

The `tcgen` function generates random values for \(N\), \(K\), and the list \(A\) according to the constraints:

- \(N\) is between 1 and 100.
- \(K\) is between 1 and \(10^5\).
- \(A\) is a sorted list of \(N\) unique integers between 1 and \(K\).

The `format_test_case` function formats the generated test case into the required input format.

When you run the `tcgen` function, it will generate a new test case each time. Here is an example of what the output might look like:

```
3 15
1 5 10
```

This means \(N = 3\), \(K = 15\), and \(A = [1, 5, 10]\).

You can use this generator to create multiple test cases to validate your solution for different scenarios.