I'm trying to understand c++ variadic templates. I'm not much aware of the correct language to use to explain what I'd like to achieve, so it might be simpler if I provide a bit of code which illustrate what I'd like to achieve.

#include <iostream>
#include <string>


using namespace std;

template<int ...A>
class TestTemplate1 {
public:
    string getString() {
        return "Normal";
    }
};

template<int T, int ...A>
string TestTemplate1<2, A...>::getString() {
    return "Specialized";
}


template<typename ...A>
class TestTemplate2 {

};

int main() {
    TestTemplate1<1, 2, 3, 4> t1_1;
    TestTemplate1<1, 2> t1_2;
    TestTemplate1<> t1_3;
    TestTemplate1<2> t1_4;

    TestTemplate2<> t2_1;
    TestTemplate2<int, double> t2_2;

    cout << t1_1.getString() << endl;
    cout << t1_2.getString() << endl;
    cout << t1_3.getString() << endl;
    cout << t1_4.getString() << endl;
}

This throws several errors.

• error C2333: 'TestTemplate1<>::getString' : error in function declaration; skipping function body
• error C2333: 'TestTemplate1<1,2,3,4>::getString' : error in function declaration; skipping function body
• error C2333: 'TestTemplate1<1,2>::getString' : error in function declaration; skipping function body
• error C2333: 'TestTemplate1<2>::getString' : error in function declaration; skipping function body
• error C2977: 'TestTemplate1' : too many template arguments
• error C2995: 'std::string TestTemplate1::getString(void)' : function template has already been defined
• error C3860: template argument list following class template name must list parameters in the order used in template parameter list

How can I have a specialized behavior for every TestTemplate1<2, ...> instances like t1_4?