Here is the test case generator for the given problem statement "E: City":

```python
import random

def tcgen():
    # Constraints
    H = random.randint(2, 10**9)
    W = random.randint(2, 10**9)
    S = random.randint(1, H)
    T = random.randint(1, W)
    
    return H, W, S, T

# Example usage
if __name__ == "__main__":
    # Generate a test case
    H, W, S, T = tcgen()
    print(f"{H} {W} {S} {T}")
```

Explanation:
- `H` is the number of rows in the city and is randomly chosen between 2 and \(10^9\).
- `W` is the number of columns in the city and is randomly chosen between 2 and \(10^9\).
- `S` is the starting row for Santa and is randomly chosen between 1 and `H`.
- `T` is the starting column for Santa and is randomly chosen between 1 and `W`.

Given this generator, you can easily create a variety of test cases to check the behavior of the problem solution under different scenarios. Note that due to the large potential values of `H` and `W`, the actual city grid is conceptual rather than something you would explicitly construct in memory for testing.