Sure, I can help you write a test case generator for the provided problem statement. Given the constraints, especially the very large bounds for `n` and `m`, our generator will produce values within these bounds, but we should be mindful of the potential computational challenges involved in generating very large numbers.

Here's a Python function to generate test cases for the problem statement "Ebi-chan and Integer Sequences":

```python
import random

def tcgen():
    # Define the modulo constant
    MOD = 10**9 + 7
    
    # Generate a random value for n within the specified bounds
    n = random.randint(1, 10**15)
    
    # Generate a random value for m within the specified bounds
    m = random.randint(0, 10**15)
    
    return n, m

# Example usage of the test case generator
n, m = tcgen()
print(f"{n} {m}")
```

This function will generate a random pair `(n, m)` where `1 ≤ n ≤ 10^15` and `0 ≤ m ≤ 10^15`. Note that due to the large range of possible values, the integers generated can be very large, and the output may not fit in standard 32-bit integers.

Please keep in mind that handling such large numbers might require efficient algorithms and data structures, especially given the constraints of competitive programming environments.