Sure, I can help you with a test case generator for your problem statement. The main task is to generate a random integer \( N \) within the given constraints and output it.

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

```python
import random

def tcgen():
    # Generate a random N within the given constraint 1 <= N < 10^9
    N = random.randint(1, 10**9 - 1)
    
    return N

# Example usage:
if __name__ == "__main__":
    test_case = tcgen()
    print(test_case)
```

This function `tcgen` will generate a random integer \( N \) between 1 and \( 10^9 - 1 \) and return it. You can call this function to generate test cases for your problem.

### Explanation:
- **N**: The integer \( N \) is randomly chosen to be between 1 and \( 10^9 - 1 \) inclusive, ensuring it meets the problem constraints.

Feel free to integrate this generator in your testing setup and generate as many test cases as you need!