Sure, I can help you create a test case generator for this problem. The generator will produce random values for \(N\) and the sequence \(A\) within the specified constraints. Here's the implementation:

```python
import random

def tcgen():
    N = random.randint(1, 2 * 10**5)
    A = [random.randint(1, 10**6) for _ in range(N)]
    
    return N, A

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

This function `tcgen` will generate a random test case each time it is called. The output format will be consistent with the input format specified in the problem statement:

1. An integer \(N\) (1 ≤ \(N\) ≤ 200,000), representing the length of the sequence.
2. A list \(A\) of size \(N\), where each integer \(A[i]\) (1 ≤ \(A[i]\) ≤ 1,000,000) represents an element of the sequence.

You can use this generator to create various test cases to thoroughly test your solution for the given problem.