For a given len length interval, suppose there are l1 positive numbers and l2 negative numbers. Now, the maximum modular sum can be obtained from the maximum of 2 values — you change as many as possible negative numbers to positive or you change as many as possible positive numbers to negative. If you cannot change all then change the k maximum by magnitude numbers. The maximum of these 2 quantities is the maximum modular sum of that interval. So for a given interval if you know the k smallest negative numbers and the k largest positive numbers and the total sum of the interval then you can find out the answer for that interval. To do this for all intervals, maintain multisets of the required values and keep on adding new and removing the oldest elements as you go, just like you do in a sliding window problem. I hope now you can understand the implementations.