```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 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")
    if least > span:
        least = span
    result = []
    while start < end:
        if start + span > end:
            span = end - start
        result.append((start, start + span))
        start += span + rest
    return result
```