@Override
  public @Nullable Entry<K, V> lowerEntry(@ParametricNullness K key) {
    return delegate().lowerEntry(key);
  }

  /**
   * A sensible definition of {@link #lowerEntry} in terms of the {@code lastEntry()} of {@link
   * #headMap(Object, boolean)}. If you override {@code headMap}, you may wish to override {@code
   * lowerEntry} to forward to this implementation.
   */

  @Override
  public @Nullable Entry<K, V> lowerEntry(@ParametricNullness K key) {
    return delegate().lowerEntry(key);
  }

  /**
   * A sensible definition of {@link #lowerEntry} in terms of the {@code lastEntry()} of {@link
   * #headMap(Object, boolean)}. If you override {@code headMap}, you may wish to override {@code
   * lowerEntry} to forward to this implementation.
   */

  private Range<K> coalescedRange(Range<K> range, V value) {
    Range<K> coalescedRange = range;
    Entry<Cut<K>, RangeMapEntry<K, V>> lowerEntry =
        entriesByLowerBound.lowerEntry(range.lowerBound);
    coalescedRange = coalesce(coalescedRange, value, lowerEntry);

    Entry<Cut<K>, RangeMapEntry<K, V>> higherEntry =
        entriesByLowerBound.floorEntry(range.upperBound);

  public void testLower() {
    resetWithHole();
    assertEquals(null, navigableMap.lowerEntry(a.getKey()));
    assertEquals(null, navigableMap.lowerKey(a.getKey()));
    assertEquals(a, navigableMap.lowerEntry(b.getKey()));
    assertEquals(a.getKey(), navigableMap.lowerKey(b.getKey()));
    assertEquals(a, navigableMap.lowerEntry(c.getKey()));
    assertEquals(a.getKey(), navigableMap.lowerKey(c.getKey()));
  }

  private Range<K> coalescedRange(Range<K> range, V value) {
    Range<K> coalescedRange = range;
    Entry<Cut<K>, RangeMapEntry<K, V>> lowerEntry =
        entriesByLowerBound.lowerEntry(range.lowerBound);
    coalescedRange = coalesce(coalescedRange, value, lowerEntry);

    Entry<Cut<K>, RangeMapEntry<K, V>> higherEntry =
        entriesByLowerBound.floorEntry(range.upperBound);

    Entry<K, V> entry = lastEntry();
    if (entry == null) {
      throw new NoSuchElementException();
    } else {
      return entry.getKey();
    }
  }

  @Override
  public @Nullable Entry<K, V> lowerEntry(@ParametricNullness K key) {
    return headMap(key, false).lastEntry();
  }

  @Override
  public @Nullable Entry<K, V> floorEntry(@ParametricNullness K key) {
    return headMap(key, true).lastEntry();
  }

                MapFeature.ALLOWS_NULL_VALUES,
                CollectionFeature.SUPPORTS_ITERATOR_REMOVE,
                MapFeature.GENERAL_PURPOSE)
            /*
             * StandardDescendingMap uses lowerEntry(), and TreeMap.lowerEntry() deliberately
             * produces immutable entries.
             *
             * TODO(cpovirk): Consider making StandardDescendingMap return a ForwardingEntry that
             * supports setValue().

    Entry<K, V> entry = lastEntry();
    if (entry == null) {
      throw new NoSuchElementException();
    } else {
      return entry.getKey();
    }
  }

  @Override
  public @Nullable Entry<K, V> lowerEntry(@ParametricNullness K key) {
    return headMap(key, false).lastEntry();
  }

  @Override
  public @Nullable Entry<K, V> floorEntry(@ParametricNullness K key) {
    return headMap(key, true).lastEntry();
  }

    return delegate.lastEntry();
  }

  @Override
  public K lastKey() {
    return delegate.lastKey();
  }

  @Override
  public @Nullable Entry<K, V> lowerEntry(K key) {
    return delegate.lowerEntry(checkValid(key));
  }

  @Override
  public @Nullable K lowerKey(K key) {
    return delegate.lowerKey(checkValid(key));
  }

  @Override

    return delegate.lastEntry();
  }

  @Override
  public K lastKey() {
    return delegate.lastKey();
  }

  @Override
  public @Nullable Entry<K, V> lowerEntry(K key) {
    return delegate.lowerEntry(checkValid(key));
  }

  @Override
  public @Nullable K lowerKey(K key) {
    return delegate.lowerKey(checkValid(key));
  }

  @Override