Generate prop paths of nested module

test.ts

// marker interface for module
interface Module {
    _module_: 1
}

type ValueOf<T> = T[keyof T];
type PropPaths<
    T, 
    K1 extends string = never,
    K2 extends string = never, 
    K3 extends string = never, 
    K4 extends string = never 
> = ValueOf<{
    [K in Exclude<keyof T, "_module_">]: (
        T[K] extends Module ? (
            K1 extends never ? PropPaths<T[K], K> :
            K2 extends never ? PropPaths<T[K], K1, K> :
            K3 extends never ? PropPaths<T[K], K1, K2, K> :
            K4 extends never ? PropPaths<T[K], K1, K2, K3, K> :
            never
        ) : (
            K1 extends never ? K :
            K2 extends never ? [K1, K] :
            K3 extends never ? [K1, K2, K] :
            K4 extends never ? [K1, K2, K3, K] :
            [K1, K2, K3, K4, K]
        )
    )
}>;

interface Test {
    foo: string;
    bar: number;
    baz: {
        _module_: 1;
        hoge: string;
        fuga: {
            _module_: 1;
            piyo: string;
            a: {
                _module_: 1;
                x: {};
            },
            b: {    // is not module
                x: {};
            }
        }
    }
}

type X = PropPaths<Test>;
// "foo" | "bar" | ["baz", "hoge"] | ["baz", "fuga", "piyo"] | ["baz", "fuga", "a", "x"] | ["baz", "fuga", "b"]