Pulverizer algorithm to find smallest linear combination of two positive numbers

pulverizer.py

def quotient_remainder(a, b):
    # returns quotient and remainder of a division b
    # a = q*b + r
    q = 0
    while a >= b:
        q += 1
        a -= b
    
    return q, a

def pulverizer(a, b):
    u0, v0 = 0, 1
    u1, v1 = None, None
    while b > 0:
        q, r = quotient_remainder(a, b)
        a, b = b, r
        
        if u1 is None:
            u1, v1 = 1, -q
        else:
            u = -q * u1 + u0
            v = -q * v1 + v0
            u0, v0 = u1, v1
            u1, v1 = u, v
            
    return a, u0, v0