Polymorphism and Interfaces

The following code did not behave as I expected. It returns "A::f" twice, but I expected it to return first "A::f", then "B::f".

There are two ways of getting the desired behavior, either declaring A.f() virtual or explicitly stating that B implements I. The latter is not desirable since I don't think B should need to know that A implements I, and the former I don't think is intuitive.

Any thoughts?

   public interface I
   {
       void f();
   }
   public class A : I
   {
       public void f() { Console.WriteLine("A::f") ;}
   }
   public class B : A
   {
       public void f() { Console.WriteLine("B::f"); }
   }
   public class C
   {
       static void Main()
       {
           I i1 = new A();
           I i2 = new B();

           i1.f();
           i2.f();
       }
   }