<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _dynamic_mul(self, dimensions, other, keys):
 """ Implements dynamic version of overlaying operation overlaying DynamicMaps and HoloMaps where the key dimensions of one is a strict superset of the other. """

        # If either is a HoloMap compute Dimension values
        if not isinstance(self, DynamicMap) or not isinstance(other, DynamicMap):
            keys = sorted((d, v) for k in keys for d, v in k)
            grouped =  dict([(g, [v for _, v in group])
                             for g, group in groupby(keys, lambda x: x[0])])
            dimensions = [d(values=grouped[d.name]) for d in dimensions]
            map_obj = None

        # Combine streams
        map_obj = self if isinstance(self, DynamicMap) else other
        if isinstance(self, DynamicMap) and isinstance(other, DynamicMap):
            self_streams = util.dimensioned_streams(self)
            other_streams = util.dimensioned_streams(other)
            streams = list(util.unique_iterator(self_streams+other_streams))
        else:
            streams = map_obj.streams

        def dynamic_mul(*key, **kwargs):
            key_map = {d.name: k for d, k in zip(dimensions, key)}
            layers = []
            try:
                self_el = self.select(HoloMap, **key_map) if self.kdims else self[()]
                layers.append(self_el)
            except KeyError:
                pass
            try:
                other_el = other.select(HoloMap, **key_map) if other.kdims else other[()]
                layers.append(other_el)
            except KeyError:
                pass
            return Overlay(layers)
        callback = Callable(dynamic_mul, inputs=[self, other])
        callback._is_overlay = True
        if map_obj:
            return map_obj.clone(callback=callback, shared_data=False,
                                 kdims=dimensions, streams=streams)
        else:
            return DynamicMap(callback=callback, kdims=dimensions,
                              streams=streams)