def collision_probability_class_5(x: int, y: int) -> float:
    """
    Positive Example 3:

    H_m = { h : x -> a * x mod 2^k div 2^k-l | a in U and a odd}

    Compute the probability that for a random hash function h from H_m,
    x and y collide under h, that is h(x) = h(y).

    This is equal to the percentage of hash functions h from H_m for
    which h(x) = h(y).

    >>> 2/16
    0.125
    >>> 1/16
    0.0625

    >>> import universal_hashing
    >>> universal_hashing.m = 16
    >>> universal_hashing.u = 128
    >>> collision_probability_class_5(1, 16)
    0.0625
    >>> collision_probability_class_5(3, 24)
    0.0625
    """

    collision_counter= 0
    number_of_iterations = 0
    l = math.log2(m)
    k = math.log2(u)
    pff =k-l +2

    for a in range (1,u,2): #a muss ungerade sein
        if str(bin(a*x))[pff:k-1] == str(bin(a*y))[pff:k-1]:
            collision_counter += 1
            print("collision")
            number_of_iterations +=1
        else:
            number_of_iterations +=1



    return (collision_counter/number_of_iterations)



"""
>>> m = 16
>>> u = 128
>>> collision_probability_class_5(1, 16)
Traceback (most recent call last):
  File "<pyshell#86>", line 1, in <module>
    collision_probability_class_5(1, 16)
  File "C:\Users\Hometown Derry\Desktop\universal hashing.py", line 222, in collision_probability_class_5
    if str(bin(a*x))[pff:k-1] == str(bin(a*y))[pff:k-1]:
TypeError: slice indices must be integers or None or have an __index__ method
>>> """