Certainly! Here is a test case generator for the problem where you are given two positive integers \(A\) and \(B\) and you need to compare their magnitudes:

```python
import random

def generate_large_number():
    # Generates a random large number with digits between 1 and 100
    length = random.randint(1, 100)
    # Ensure the number does not start with zero
    number = str(random.randint(1, 9))
    number += ''.join(random.choices('0123456789', k=length-1))
    return number

def tcgen():
    A = generate_large_number()
    B = generate_large_number()
    
    return A, B

# Example usage
A, B = tcgen()
print(A)
print(B)
```

This function will generate two random large numbers \(A\) and \(B\) with lengths between 1 and 100 digits, ensuring they do not start with a zero. 

Example output when running the generator:

```
573829374828392938475
283948293847293847
```

You can use the generated values to test the comparison logic in your competitive programming solution.