Sure, I can help you with that. Here's a test case generator for the given problem statement "SolveMe":

```python
import random

def tcgen():
    N = random.randint(1, 1000)
    X = random.randint(0, 10**18)
    Y = random.randint(0, 10**18)
    Z = random.randint(0, 10**18)
    
    return N, X, Y, Z

# Example usage:
N, X, Y, Z = tcgen()
print(f"{N} {X} {Y} {Z}")
```

This function generates random test cases within the specified constraints:

- \(N\) is a random integer between 1 and 1000 inclusive.
- \(X\), \(Y\), and \(Z\) are random integers between 0 and \(10^{18}\) inclusive.

The `tcgen` function returns these values as a tuple, which you can use to test your solution to the "SolveMe" problem. Here is an example of how you could use the generated values:

```python
# Example usage:
N, X, Y, Z = tcgen()
print(f"Generated Test Case: N={N}, X={X}, Y={Y}, Z={Z}")
```

By running this code multiple times, you will get different test cases that you can use for your competitive programming problem.