Call function with defaulted parameters through function pointer

I want to write a function template run that calls a passed callable which takes no parameters and prints its return value if it is not void. Here is my attempt:

template<typename FUNC>
void run(FUNC &&f)
{
  if constexpr (std::is_void_v<decltype(f())>)
    f();
  else
    std::cout << f() << std::endl;
}

Now here is the problem: I would like run to accept functions that do take parameters which all have a default value, i.e.:

int foo()
{ return 0; }

int bar(int a = 1, int b = 2)
{ return a + b; }

template<typename FUNC>
void run(FUNC &&f)
{
  if constexpr (std::is_void_v<decltype(f())>)
    f();
  else
    std::cout << f() << std::endl;
}

int main()
{
  run(foo);
  run(bar); // compiler error, too few arguments to f()
}

This does not work yet since default parameters are not part of a functions signature and so I can't call f() inside run. How can I fix this?