Guice: Building Related Trees of Objects / Robot Legs

I have a class A that holds a class B like this:

class A {
   private final B b;
   @Inject
   A(B b) {
     this.b = b;
   }
}

interface B {}
class B1 implements B {}
class B2 implements B {}

class Client() {
   @Inject 
   Client(@AhasB1 A aHasB1, @AhasB2 A aHasB2) { }
}

I'd like to bind two different A's, one annotated @AhasB1 and another @AhasB2. How can I bind these correctly?

Here's how I did it using PrivateModule.

public class MainModule extends AbstractModule {
    @Override
    protected void configure() {
        install(new PrivateModule(){
            @Override
            protected void configure() {
                bind(A.class).annotatedWith(AhasB1.class).to(A.class);
                expose(A.class).annotatedWith(AhasB1.class);
                bind(B.class).to(B1.class);
            }
        });

        install(new PrivateModule(){
            @Override
            protected void configure() {
                bind(A.class).annotatedWith(AhasB2.class).to(A.class);
                expose(A.class).annotatedWith(AhasB2.class);
                bind(B.class).to(B2.class);
            }
        });
}