Certainly! Here is a test case generator for the provided problem statement:

```python
import random

def tcgen():
    X = random.randint(1, 10**9)
    t = random.randint(1, 10**9)
    
    return X, t

# Example usage:
if __name__ == "__main__":
    test_case = tcgen()
    print(test_case)
```

This code snippet generates random test cases for the given problem statement. The function `tcgen()` generates two random integers \(X\) and \(t\) within the given constraints (1 ≤ \(X\) ≤ 10^9 and 1 ≤ \(t\) ≤ 10^9).

You can use this generator to produce multiple test cases for thorough testing of your solution. Here is how the output might look:

```
(1000000000, 1000000000)
(48, 58)
(100, 17)
```

You can run this generator multiple times to produce different test cases each time.