Certainly! The problem statement you've provided is significantly more complex than the earlier example, primarily due to the very large constraints on \( M \) and \( N \). However, I'll write a test case generator that follows the problem constraints.

Here's the test case generator for "Problem H: Count Words":

```python
import random

def tcgen():
    # Generate M in the range [1, 10^18]
    M = random.randint(1, 10**18)
    
    # Generate N in the range [1, 10^18]
    N = random.randint(1, 10**18)
    
    # Generate K in the range [1, 1000]
    K = random.randint(1, 1000)
    
    return M, N, K

# Example usage
for _ in range(5):  # Generate 5 test cases
    M, N, K = tcgen()
    print(f"{M} {N} {K}")

```

This generator will produce valid random test cases according to the constraints specified in the problem statement. When using this generator, keep in mind that \( M \) and \( N \) can be extremely large, so handling them properly in your solution is critical.