[Typescript] 150 Hard - OptionalUndefined

Implement the util type OptionalUndefined<T, Props> that turns all the properties of T that can be undefined, into optional properties. In addition, a second -optional- generic Props can be passed to restrict the properties that can be altered.

OptionalUndefined<{ value: string | undefined, description: string }>
// { value?: string | undefined; description: string }

OptionalUndefined<{ value: string | undefined, description: string | undefined, author: string | undefined }, 'description' | 'author'>
// { value: string | undefined; description?: string | undefined, author?: string | undefined }

Solution:

/* _____________ Your Code Here _____________ */

type Merge<T> = {
  [K in keyof T]:T[K]
}

type OptionalUndefined<
  T, 
  Props extends keyof T = keyof T,
  OptionsProps extends keyof T = Props extends keyof T
    ? undefined extends T[Props]
      ? Props
      :never 
    :never
> = 
  Merge<{
    [K in OptionsProps]?: T[K]
  } & {
    [K in Exclude<keyof T, OptionsProps>]: T[K]
  }>

/* _____________ Test Cases _____________ */
import type { Equal, Expect } from '@type-challenges/utils'
import { ExpectFalse, NotEqual } from '@type-challenges/utils'

type cases = [
  Expect<Equal<OptionalUndefined<{ value: string | undefined }, 'value'>, { value?: string | undefined }>>,
  Expect<Equal<OptionalUndefined<{ value: string; desc: string }, 'value'>, { value: string; desc: string }>>,
  Expect<Equal<OptionalUndefined<{ value: string | undefined; desc: string }, 'value'>, { value?: string; desc: string }>>,
  Expect<Equal<OptionalUndefined<{ value: string | undefined; desc: string | undefined }, 'value'>, { value?: string | undefined; desc: string | undefined }>>,
  Expect<Equal<OptionalUndefined<{ value: string | undefined; desc: string }, 'value' | 'desc'>, { value?: string; desc: string }>>,
  Expect<Equal<OptionalUndefined<{ value: string | undefined; desc: string | undefined }>, { value?: string; desc?: string }>>,
  Expect<Equal<OptionalUndefined<{ value?: string }, 'value'>, { value?: string }>>,
  Expect<Equal<OptionalUndefined<{ value?: string }>, { value?: string }>>,
]