Sure! Here's a Python function to generate test cases for the given problem statement for "SolveMe":

```python
import random

def tcgen():
    # Generate random values for N, X, Y, and Z within the specified constraints
    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 of generating a test case
N, X, Y, Z = tcgen()
print(f"{N} {X} {Y} {Z}")
```

This function randomly generates the values for \(N\), \(X\), \(Y\), and \(Z\) within their respective constraints. Each time you call `tcgen()`, it will return a new set of input parameters for the problem.

Here is how you might use this function:

```python
for _ in range(5):  # Generate 5 test cases
    N, X, Y, Z = tcgen()
    print(f"Test Case: N={N}, X={X}, Y={Y}, Z={Z}")
```

You can adjust the loop to generate as many test cases as you need. The generated values will help ensure your solution is robust and can handle a variety of inputs within the specified constraints.