```python
def window_max(readings: list[int], width: int) -> list[int]:
    """
    Returns the largest reading in every stretch of the given width.
    """
    if width <= 0:
        raise ValueError("Width must be greater than zero.")
    
    if not readings or width > len(readings):
        return []
    
    max_values = []
    for i in range(len(readings) - width + 1):
        max_value = max(readings[i:i + width])
        max_values.append(max_value)
    
    return max_values
```