```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")
    # Walk the shift, cutting a stretch of at most span units, then
    # skipping rest units, dropping a final stretch shorter than least.
    result = []
    current_start = start
    while current_start < end:
        stretch_length = min(span, end - current_start)
        result.append((current_start, current_start + stretch_length))
        current_start += stretch_length + rest
    return result
```