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    Honestly, some puzzles just aren't worth the time / points. This one looks like it's just bookkeeping.

    Running the range and doing pop-counts takes too long. Instead, given the range, determine how often each of the 32-bits possible will be a 1. The range may contain some number of full cycles, with half 1s and half 0s, and then some off-cycle handling on either end. Might have to handle a case for the positive portion of the range and a case for the negatives -- TBD.