Sure! Below is a test case generator for the given problem statement. This generator will produce random inputs according to the constraints provided:

```python
import random

def generate_test_case():
    # Define constraints
    MIN_N = 2
    MAX_N = 10**6
    MOD = 10**9 + 7
    
    # Randomly determine the size of N
    N = random.randint(MIN_N, MAX_N)
    
    return N

# Example usage of the test case generator
if __name__ == "__main__":
    print(generate_test_case())
```

This generator will create a random test case for the problem where \(N\) is a random integer between 2 and \(10^6\). The generated test case can then be used to test implementations of the problem.

For more complex testing, especially to test edge cases, you might want to include specific values for \(N\) such as the minimum (2) and maximum (\(10^6\)) values:

```python
def generate_edge_cases():
    edge_cases = [2, 10**6]
    return edge_cases

# Example usage of the edge case generator
if __name__ == "__main__":
    for case in generate_edge_cases():
        print(case)
```

This will output edge cases of the problem, ensuring that your implementation can handle the smallest and largest inputs as specified by the constraints.