Build Your Own range

range(0, 10 ** 18, 7) holds about 142 quadrillion numbers, yet it takes almost no memory and answers questions about them instantly. Build MyRange, a class that does the same, without using the built-in range.

• MyRange(stop), MyRange(start, stop) and MyRange(start, stop, step) mean the same as with range: the numbers start, start + step, start + 2 * step and so on, stopping before stop. When step is negative, the numbers go down and stop before going down to stop. start is 0 and step is 1 when they are not given. A step of 0 raises ValueError.
• iter(r) (and so a for loop, or list(r)) gives the numbers in order. A MyRange can be looped over any number of times, and each loop starts from the beginning.
• len(r) returns how many numbers there are.
• r[i] returns the number at index i; negative indexes count from the end. An index outside the range raises IndexError.
• x in r is True when the whole number x is one of the numbers.

len, r[i] and in must answer at once, even for ranges of 10^18 numbers.

Examples

list(MyRange(5))               # [0, 1, 2, 3, 4]
list(MyRange(2, 12, 3))        # [2, 5, 8, 11]

r = MyRange(10, 0, -3)
list(r)                        # [10, 7, 4, 1]
len(r)                         # 4
r[-1]                          # 1
4 in r, 5 in r                 # (True, False)

Constraints

• All arguments, indexes and the x in x in r are integers
• start and stop can be anywhere between -10^18 and 10^18

Note

The Python in your browser is 32-bit: len() there cannot go past 2,147,483,647, even for the built-in range. The tests ask len() only of smaller ranges; indexing and in are tested on the giant ones, so work out the size with your own arithmetic there instead of calling len(self).