Sure, let's create a test case generator for the given problem statement. The given problem involves generating a number of piles with a specified number of stones in each pile. Here's a Python function to generate random test cases for this problem:

```python
import random

def tcgen():
    # Generate a random number of piles within the constraint
    N = random.randint(2, 300)
    
    # Generate a list of N pile sizes where each pile has a random number of stones within the constraint
    A = [random.randint(1, 10**12) for _ in range(N)]
    
    return N, A

# Example of generating a test case
N, A = tcgen()
print(N)
print(" ".join(map(str, A)))
```

This function generates a random number of piles \(N\) (between 2 and 300), and for each pile, it assigns a random number of stones \(A[i]\) (between 1 and \(10^{12}\)). 

You can use this function to produce random test cases for your problem. Each time you call `tcgen()`, it will produce a new, random test case that adheres to the given constraints, ensuring a variety of test cases to validate your solution.

Here's an example of how to use the generated test cases:

```python
# Example usage of the generated test case
N, A = tcgen()
print("Generated Test Case:")
print(f"N: {N}")
print(f"A: {A}")
```

This will print out the generated values for \(N\) and \(A\), which you can then use to test your solution to the problem.