Checking for existence of an (overloaded) member function

There are a number of answered questions about checking whether a member function exists: for example, Is it possible to write a C++ template to check for a function's existence?

But this method fails, if the function is overloaded. Here is a slightly modified code from that question's top-rated answer.

#include <iostream>
#include <vector>

struct Hello
{
    int helloworld(int x)  { return 0; }
    int helloworld(std::vector<int> x) { return 0; }
};

struct Generic {};


// SFINAE test
template <typename T>
class has_helloworld
{
    typedef char one;
    typedef long two;

    template <typename C> static one test( decltype(&C::helloworld) ) ;
    template <typename C> static two test(...);


public:
    enum { value = sizeof(test<T>(0)) == sizeof(char) };
};


int
main(int argc, char *argv[])
{
    std::cout << has_helloworld<Hello>::value << std::endl;
    std::cout << has_helloworld<Generic>::value << std::endl;
    return 0;
}

This code prints out:

0
0

But:

1
0

if the second helloworld() is commented out.

So my question is whether it's possible to check whether a member function exists, regardless of whether it's overloaded.