How to indicate the overloaded function of given signature in std::bind?

I have api function f_api(std::function<void(int)> func) and now I have my process class

class Func {
public:
    void operator()(int i) {
        // do some work
    }
    int operator()(int i, int j) {
        // do some other work
    }
};

and I want use Func f f(int i) to pass to f_api to do the work; so I use std::bind

Func f;
std::function<void(int)> func = std::bind(&Func::operator(), &f, std::placeholders::_1);
f_api(func);

but HERE the problem, How can I indicate which Func::operator()() I want to bind? I can give a member function by its name, but how can I process this when this member function do have several different signed reloading functions? Will std::bind find me the most suitable function to be called? C++ is so complicated.....

the minimal verifiable case:

#include <iostream>
#include <functional>

using namespace std;

class Func {
public:
    void operator()(int i) {
        // do some work
        cout << "i is: " << i << endl;
    }
    int operator()(int i, int j) {
        // do some other work
    }
};

void f_api(function<void(int)> f) {
    f(3);
}

int main () {
    Func f;
    std::function<void(int)> func = std::bind(&Func::operator(), &f, std::placeholders::_1);
    f_api(func);
    return 0;
}

the compiling error:

a.cpp: In function ‘int main()’:
a.cpp:23:91: error: no matching function for call to ‘bind(<unresolved overloaded function type>, Func*, const std::_Placeholder<1>&)’
     std::function<void(int)> func = std::bind(&Func::operator(), &f, std::placeholders::_1);
                                                                                           ^
a.cpp:23:91: note: candidates are:
In file included from a.cpp:2:0:
/usr/include/c++/4.8/functional:1655:5: note: template<class _Func, class ... _BoundArgs> typename std::_Bind_helper<std::__or_<std::is_integral<typename std::decay<_Tp>::type>, std::is_enum<typename std::decay<_Tp>::type> >::value, _Func, _BoundArgs ...>::type std::bind(_Func&&, _BoundArgs&& ...)
     bind(_Func&& __f, _BoundArgs&&... __args)
     ^
/usr/include/c++/4.8/functional:1655:5: note:   template argument deduction/substitution failed:
a.cpp:23:91: note:   couldn't deduce template parameter ‘_Func’
     std::function<void(int)> func = std::bind(&Func::operator(), &f, std::placeholders::_1);
                                                                                           ^
In file included from a.cpp:2:0:
/usr/include/c++/4.8/functional:1682:5: note: template<class _Result, class _Func, class ... _BoundArgs> typename std::_Bindres_helper<_Result, _Func, _BoundArgs>::type std::bind(_Func&&, _BoundArgs&& ...)
     bind(_Func&& __f, _BoundArgs&&... __args)
     ^
/usr/include/c++/4.8/functional:1682:5: note:   template argument deduction/substitution failed:
a.cpp:23:91: note:   couldn't deduce template parameter ‘_Result’
     std::function<void(int)> func = std::bind(&Func::operator(), &f, std::placeholders::_1);
                                                                                           ^

And in my case it's a little bit different cause my class Func cannot be assigned cause one member field of that class is not assignable, so I will get a slightly different error during the compiling time.