nextPowerOfTwo <<= 1;
        bits++;
      }
      // Get rid of the 2s in num.
      int tz = Long.numberOfTrailingZeros(num);
      long normalizedNum = num >> tz;
      shift += tz;
      // Adjust floor(log2(num)) + 1.
      int normalizedBits = bits - tz;
      // If it won't fit in a long, then we store off the intermediate product.
      if (normalizedBits + productBits >= Long.SIZE) {

    three_months_commenters = Counter[str]()
    six_months_commenters = Counter[str]()
    one_year_commenters = Counter[str]()
    authors: dict[str, Author] = {}

    now = datetime.now(tz=timezone.utc)
    one_month_ago = now - timedelta(days=30)
    three_months_ago = now - timedelta(days=90)
    six_months_ago = now - timedelta(days=180)
    one_year_ago = now - timedelta(days=365)