How to write a variadic template recursive function?

I'm trying to write a variadic template constexpr function which calculates sum of the template parameters given. Here's my code:

template<int First, int... Rest>
constexpr int f()
{
    return First + f<Rest...>();
}

template<int First>
constexpr int f()
{
    return First;
}

int main()
{
    f<1, 2, 3>();
    return 0;
}

Unfortunately, it does not compile reporting an error message error C2668: 'f': ambiguous call to overloaded function while trying to resolve f<3,>() call.

I also tried to change my recursion base case to accept 0 template arguments instead of 1:

template<>
constexpr int f()
{
    return 0;
}

But this code also does not compile (message error C2912: explicit specialization 'int f(void)' is not a specialization of a function template).

I could extract first and second template arguments to make this compile and work, like this:

template<int First, int Second, int... Rest>
constexpr int f()
{
    return First + f<Second, Rest...>();
}

But this does not seem to be the best option. So, the question is: how to write this calculation in an elegant way?

UP: I also tried to write this as a single function:

template<int First, int... Rest>
constexpr int f()
{
    return sizeof...(Rest) == 0 ? First : (First + f<Rest...>());
}

And this also does not work: error C2672: 'f': no matching overloaded function found.