Isomorphic object map in TypeScript

Question

I'm trying write a well-typed equivalent of lodash's mapValues which will have a return type with the same shape the original object, not just a Record<x,y>.

Given a source object:

const orig = {
  a: {
    get: () => "foo",
  },
  b: {
    get: () => 5,
  },
  c: {
    get: () => true,
  }
};

Then mapValues(x => x.get(), orig) would return

{
  a: "foo",
  b: 5,
  c: true,
}

And its type would be

{
  a: string,
  b: number,
  c: boolean
}

My first effort is generic on the respective values:

export const mapValues = <V1, V2>(
  f: (v: V1) => V2,
  obj: {[k: string]: V1},
): {[k: string]: V2} => {
  const result: {[k: string]: V2} = {};
  for (const k in obj) {
    result[k] = f(obj[k]);
  }
  return result;
};

But the type ends up being

{
    [k: string]: string | number | boolean;
}

My best effort so far (which doesn't compile) is:

export const mapValues2 = <TInput, TOutput>(
  f: <K extends keyof TInput>(v: TInput[K]) => (K extends keyof TOutput) ? TOutput[K] :never,
  obj: TInput,
): TOutput => {
  const result: Partial<TOutput> = {};
  for (const k in obj) {
    result[k] = f<typeof k>(obj[k]);
  }
  return result as TOutput;
};

I have a playground here.