Pullback perserving functor

Would someone let me know the answer and the proof or counter example of the following question? Suppose the category C has a pullback for every pair of morphism (f : X -> Y, g : W -> Y). Let K be the full subcategory of the functor category Func(C,Set) whose objects are pullback perserving functors. Is K ccc? (If so, how I can show this?) Thanks, Hongseok