def slow_gcd(x,y):
    """ greatest common divisor of two integers - naive inefficient method """

    assert isinstance(x,int) and isinstance(y,int) # type checking: x and y both integers
    x,y = abs(x),abs(y) # simultaneous assignment to x and y
            # gcd invariant to abs. Both x,y now non-negative
    if x<y:
        x,y = y,x   # switch x and y if x < y. Now y <= x

    for g in range(y, 0, -1): # from x downward to 1
        if x%g == y%g == 0:  # g divides both x and y?
            return g
    return None # should never get here, 1 divides all
    


def gcd(x,y):
    """ greatest common divisor of two integers - Euclid's algorithm """

    assert isinstance(x,int) and isinstance(y,int) # type checking: x and y both integers
    x,y = abs(x),abs(y) # simultaneous assignment to x and y
            # gcd invariant to abs. Both x,y now non-negative
    if x<y:
        x,y = y,x   # switch x and y if x < y. Now y <= x

    while y>0:
        x,y = y,x%y
    return x


def display_gcd(x,y):
    """ greatest common divisor of two integers - Euclid's algorithm
        Function prints all intermediate results along the way """

    assert isinstance(x,int) and isinstance(y,int) # type checking: x and y both integers
    x,y = abs(x),abs(y) # simultaneous assignment to x and y
            # gcd invariant to abs. Both x,y now non-negative
    if x<y:
        x,y = y,x   # switch x and y if x < y. Now y <= x
    print(x,y)
    while y>0:
        x,y = y,x%y
        print(x,y)
    return x