def binary(x: int, pre: str='0b', length: int=8):
    """
    Return the binary representation of integer x
    Input:
        x: an integer of any size
        pre: the prefix for the output string, default 0b
        length: length of the output in binary if its representation has smaller length
                default is 8 i,e, 2**8=256 int, a byte
    Return:
        The binary representation of integer x with a minimum lenght of "length"
        padded with trailing 0s
    """
    return '{0}{{:{1}>{2}}}'.format(pre, 0, length).format(bin(x)[2:])