Initialize a base class member variable in derived class with some conditions

Initialize a base class member variable in derived class with some conditions

I have a requirement where I want to initialize a Base class member in
derived class.
class SuperBase
{
public:
virtual void Set();
};
class Base:public SuperBase
{
protected:
int *pVal;
public:
void Set()
{
//Some Logic
}
};
class Derived1: public Base
{
public:
// I want to Initialize Base::pVal here and after
// that I want to have this value in Set() of Base.
};
class Derived2: public Base
{
//...Same functionality as Derived1;
//...
};
int main()
{
SuperBase *s = new Derived1;
// Here when I create a Derived1 object automatically,
// the value for pVal will be initialized
s->Set();
//After calling this Set, I want to get the pVal value access in Set.
}
I know that it is an easy thing to do. But these are the things which I
cannot use for this problem:
I cannot use Constructor Initializer List for passing values from derived
class to Base [I know that I can easily do this through Constructor
Initialiser List but there is a requirement where I don't want the
existing Class Constructor]
I have tried using CRTP[curiously recurring template pattern], but that is
also not suitable as it uses a type of static binding, and in higher view,
I have to decide at run time which class object to call Derived1,Derived2.
I also don't want to write any get() in Derived1,Derived2 as I want to
only assign values there. This is also a part of my requirement.
Any Suggestions??? Any Design Patterns??