Certainly! Below is a test case generator for the given problem statement. This generator will create random values for \(A\), \(B\), \(H\), and \(M\) according to the constraints specified.

```python
import random

def tcgen():
    A = random.randint(1, 1000)
    B = random.randint(1, 1000)
    H = random.randint(0, 11)
    M = random.randint(0, 59)
    
    return A, B, H, M

# Example of generating a test case
if __name__ == "__main__":
    A, B, H, M = tcgen()
    print(f"{A} {B} {H} {M}")
```

### Explanation:

- `A` and `B` are generated randomly between 1 and 1000 inclusive, representing the lengths of the hour and minute hands, respectively.
- `H` is generated randomly between 0 and 11 inclusive, representing the hour on the clock.
- `M` is generated randomly between 0 and 59 inclusive, representing the minutes on the clock.

### Example Output:

Running the generator might give you output like:
```
715 932 4 37
```

You can use this output as an input for your program to test its correctness. Each time you run the generator, it will produce different values, giving you a wide variety of test cases.