```python
from typing import List, Tuple

def menu_pick(dishes: List[Tuple[str, int]], budget: int) -> List[str]:
    if budget < 0:
        return []
    
    dishes = sorted(dishes, key=lambda x: (budget - (prices := sum([price for _, price in dishes])), prices), 0, 0), [name, price) for name, price in dishes)))
    return [name for name, price in dishes if price <= budget]
 [name, price) for name, price in dishes if price <= budget])
```