public T lower(long sequence, boolean inclusive) {
    Entry<Long, T> lower = index.floorEntry(sequence);
    if (lower == null) {
      return null;
    }

    if (inclusive) {
      return lower.getValue();
    }

    if (lower.getKey() == sequence) {
      return lower.getValue().prev;
    } else {
      return lower.getValue();
    }
  }