```python
def fit_budget(prices: list, budget: int) -> int:
    if budget < 0:
        raise ValueError("Amount cannot be negative")
    
    if not prices:
        return 0
    
    prices.sort()
    count = 0
    for price in prices:
        if budget >= price:
            budget -= price
            count += 1
        else:
            break
    
    return count
```