C++ conditional construction of template type

I would like to be able to do something like the following:

struct A {};

template<typename T, typename U> struct B : public A {};

std::unique_ptr<A> chooseB(int i, int j)
{
  // return B<T, U> where T and U vary with i and j (0 = int, 1 = double etc.) 
}

Potentially the list of types could be long enough that just forming a big conditional that enumerates all possible pairs of i and j could be painful.

Is there are nice way to write the chooseB function? I might potentially want to generalize this to more than two template parameters.