forcing a template function to treat integers as doubles, or the type with higher precision [duplicate]

This question already has an answer here:

• How to implement generic max function? 5 answers

This question can be stupid depending how you would look at it.

Out of curiosity I wanted to implement a get_max function which can return the maximum of two similar or distinct types. I know std already has this but:

template <class T, class U>
T get_max(T lh, U rh) {
    if(lh >= rh) return lh;
    else return rh;
}

Somewhere in the main:

int a = 10;
double d = 20.01;
std::cout << "a=" << a << "\nd=" << d << "\nget_max=" <<
    get_max(a,d) << std::endl;

The result surprised me:

a=10
d=20.01
get_max=20

I was expecting to have get_max to output 20.01, but it outputed an int. I can understand because the first argument is int then the T in the function returns T which in this case is obviously int so the function returns the bigger of the two arguments, but casts it to the type of the first argument.

Is there a way to somehow make the code smart to return the double or the type with higher precision?

I know for a fact that passing the double as the first argument would be a naive way of fixing the problem!