Sure, I can help you write a test case generator for the given problem statement. Here is the Python code for the test case generator:

```python
import random

def tcgen():
    A = random.randint(-10**9, 10**9)
    
    # Ensure B is different from A
    B = A
    while B == A:
        B = random.randint(-10**9, 10**9)
    
    V = random.randint(1, 10**9)
    W = random.randint(1, 10**9)
    T = random.randint(1, 10**9)
    
    return A, V, B, W, T

# Example of how to use the generator
A, V, B, W, T = tcgen()
print(f"{A} {V}")
print(f"{B} {W}")
print(f"{T}")
```

### Explanation:
1. **A and B**: Random integers are generated between -10^9 and 10^9 for both A and B, ensuring that they are different.
2. **V and W**: Random integers are generated between 1 and 10^9 for V and W.
3. **T**: A random integer is generated between 1 and 10^9 for T.

This generator ensures that the constraints are met and produces valid input for the problem. The `while` loop ensures that A and B are different. Here is how you can use the generator and get an example of the input format.