Certainly! Here is the test case generator for the given problem statement:

```python
import random

def tcgen():
    # Constraints
    N = random.randint(1, 100)
    K = random.randint(1, 100)
    
    return N, K

# Example usage
if __name__ == "__main__":
    test_cases = [tcgen() for _ in range(10)]
    for i, (N, K) in enumerate(test_cases):
        print(f"Sample Input {i+1}")
        print(f"{N} {K}")
        # Optionally, you can also call the solution function to print the expected output.
        # For now, we just print the inputs.
```

This generator will create random test cases for the problem ensuring that values of \(N\) and \(K\) are within the given constraints (1 ≤ \(N, K\) ≤ 100). Each call to `tcgen()` will return a tuple (N, K) representing a test case.

You can run this script and it will generate multiple sample inputs, which you can use to test your solution.