C++ Template function returning type based on template arguments

I'd like to create function that creates different types of generators (own classes) and I go with something like this:

template <typename Iterator>
class Generator {
Iterator begin_;
Iterator end_;
public:
Generator(Iterator begin, Iterator end)
    : begin_(begin)
    , end_(end)
    {}
};

template <typename GeneratorType, typename ContainerIterator>
GeneratorType<ContainerIterator> make_generator(ContainerIterator begin, ContainerIterator end){ // Error occurs here
    return GeneratorType<ContainerIterator>(std::forward<ContainerIterator>(begin), std::forward<ContainerIterator>(end));
}

But it's not compiling since error:

error: 'GeneratorType' is not a template (in line GeneratorType<ContainerIterator> make_generator...)

Do anyone know if it is possible and if yes how to fix it?