Sure! Here's a test case generator for the given problem statement:

```python
import random

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

# Example of generating a test case
if __name__ == "__main__":
    X, t = tcgen()
    print(X, t)
```

This generator function will produce random values for \(X\) and \(t\) within the given constraints (1 ≤ \(X\) ≤ 10^9 and 1 ≤ \(t\) ≤ 10^9). When you run the code, it will print a randomly generated test case in the format required by the problem statement.