In pure Python this seems to be the better option to compute inverses:

def modinv(a, m):  # assuming m > 0
    b = m
    s, s1 = 1, 0
    while b:
        a, (q, b) = b, divmod(a, b)
        s, s1 = s1, s - q * s1
    if a != 1:
        raise ValueError('inverse does not exist')
    return s if s >= 0 else s + m

Binary xgcd algorithms coded in pure Python run much slower.