Sure, I can help you write a test case generator for the "Zero AND Subsets" problem. The generator will produce random inputs that adhere to the constraints provided in the problem statement. Here is a Python function for generating such test cases:

```python
import random

def tcgen():
    N = random.randint(1, 10**5)
    A = [random.randint(0, 2**20 - 1) for _ in range(N)]
    
    return N, A

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

### Explanation:

1. **N Generation**: 
   - `N` is chosen randomly between 1 and \(10^5\), inclusive, as specified in the problem constraints.
   
2. **A Generation**:
   - The list `A` of size `N` is generated where each element is a random integer between 0 and \(2^{20} - 1\) (inclusive), also as per the problem constraints.
   
### Example Output:
Running the `tcgen` function might produce an output like this:
```
5
542 12345 678 9 1024
```

This represents:
- **N = 5**
- **A = [542, 12345, 678, 9, 1024]**

You can run the function multiple times to generate different test cases for your problem. This function ensures that all generated test cases adhere to the provided constraints.