```python
"""Work stretches of a shift: span-long, rest-separated, short tails dropped."""


def carve_shift(start: int, end: int, span: int, rest: int, least: int) -> list:
    for value in (start, end, span, rest, least):
        if isinstance(value, bool) or not isinstance(value, int):
            raise ValueError("every argument must be an integer")
    if start >= end:
        raise ValueError("shift start must precede its end")
    if span < 1 or rest < 1:
        raise ValueError("span and rest must be at least 1")
    if least < 1 or least > span:
        raise ValueError("least must be between 1 and span")
    
    stretches = []
    while start < end:
        stretch_end = min(start + span, end)
        if stretch_end - start >= least:
            stretches.append((start, stretch_end))
        start = stretch_end + rest
    
    return stretches
```