Create a generator that produces factorials. The first value returned is $1!$, the second $2!$, the third $3!$, etcetera, up to $10!$. Do not calculate the factorial every time from scratch, but retain the value that you used in the previous cycle and use that.

Assignment

Write a generator function factorials that takes one optional argument count (int), defaulting to 10. The generator yields $1!, 2!, 3!, \ldots$ up to and including count$!$, in that order. If count is 0, the generator yields nothing.

As explained above, each yielded value must be derived from the previous one (by multiplying it with the next integer), rather than recomputing the factorial from scratch every time.

Example

>>> list(factorials())
[1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]

>>> list(factorials(5))
[1, 2, 6, 24, 120]

>>> list(factorials(0))
[]