from typing import Tuple


def alpha_beta_electrons(nele: int, m_s: int) -> Tuple[int, int]:
    """Given the total number of electrons and the z-spin quantum number, return
    the number of alpha and beta electrons in the system.

    Args:
        nele (int) - number of electrons
        m_s (int) - spin angular momentum on the z-axis

    Return:
        number of alpha electrons (int), number of beta electrons (int)
    """
    if nele < 0:
        raise ValueError('Cannot have negative electrons')
    if nele < abs(m_s):
        raise ValueError('Spin quantum number exceeds physical limits')
    nalpha = int(nele + m_s) // 2
    nbeta = nele - nalpha
    return nalpha, nbeta