multiple classes in a single file : modifier private not allowed here

I am not able to understand why this code doesn't compile:

class A {
    public static void main(String[] args) {
        System.out.println("hi");
    }
}

private class B {
    int a;
}

I am saving the contents in a file named A.java - and I get an error:

modifier private not allowed here // where I have defined class B

This happens both when I try B as private and protected. Can someone please explain me the reason behind this?

Thanks !