fedecz/puzzle ? reverse-engineered prompt

Build me a small Java solution for this number puzzle.

I have the numbers from 1 to n, and for each number I want to take the product of the previous C numbers, or just whatever previous numbers are available if there are fewer than C of them. Then I want the sum of all those products across the whole range.

For example, if n is 5 and C is 2, the terms would be 0, 1, 2, 6, and 12, which adds up to 21.

Please implement this in Java, and tell me the answer for n = 100 and C = 10. Also calculate the result for n = 1000000 and C = 200, but only give me the first 10 digits of that answer.

I’d also like a quick explanation of the algorithm you used and its time complexity. If there’s a smarter way to handle very large n like 10000000 with C = 200, please include that too. If you need to look up anything current online, feel free to do that.