I have an Mapped Type, and want to implement a function which receive params as the key of MappedType, return the MappedType of key, however the code occurs an error.

type MappedType = {
  a: {
    a: string;
  };
  b: {
    b: number;
  }
};

function getValue<T extends keyof MappedType>(key: T): MappedType[T] | undefined {
  if (key === 'a') {
    // here get error
    // Type '{ a: string; }' is not assignable to type 'MappedType[T]'.
    //   Type '{ a: string; }' is not assignable to type '{ a: string; } & { b: number; }'.
    //    Property 'b' is missing in type '{ a: string; }' but required in type '{ b: number; }'.
    return {
       a: '2'
    };
  }
  return;
}

how to infer the type successfully?