To create a test case generator for the problem "Ebi-chan and Integer Sequences," we need to generate values for \( n \) and \( m \) within their specified constraints. Here's a Python function that generates random test cases for this problem:

```python
import random

def tcgen():
    # Generate n in the range from 1 to 10^15
    n = random.randint(1, 10**15)
    
    # Generate m in the range from 0 to 10^15
    m = random.randint(0, 10**15)
    
    return n, m

# Example usage:
n, m = tcgen()
print(n, m)
```

This function generates a random integer \( n \) between 1 and \( 10^{15} \) and a random integer \( m \) between 0 and \( 10^{15} \). These values will be used as inputs for the problem statement.

To ensure the function works correctly, you can run the example usage which will print one set of generated test inputs to verify their correctness.

Please note that this test case generator can generate very large values, so ensure your environment can handle such large integers before running it.