Certainly! Here's a test case generator for the given problem statement:

```python
import random

def tcgen():
    # Constraints
    N = random.randint(2, 200000)
    
    # Generate the arrays A and B
    A = [random.randint(0, 10**12) for _ in range(N)]
    B = [random.randint(0, 100) for _ in range(N)]
    
    return N, A, B

# Example usage:
N, A, B = tcgen()
print(N)
print(" ".join(map(str, A)))
print(" ".join(map(str, B)))
```

This generator function creates random inputs within the specified constraints:
- \(N\) is randomly chosen between 2 and 200,000.
- Each element of \(A\) is a random integer between 0 and \(10^{12}\).
- Each element of \(B\) is a random integer between 0 and 100.

The `print` statements at the end demonstrate how to use the generator to produce a test case and format it appropriately for input. Adjust the example usage section as needed to integrate with your testing framework or code environment.