merge 2 objects includes their children in js

Question

I have 2 objects and I am trying to merge 2 objects.

const obj = { 
  a: {}, 
  b: {}, 
  c: { 
    ca: {}, 
    cb: {}, 
    cc: {}
  }
};

const obj2 = { 
  a: {
    aa: {}
  }, 
  c: {
    cd: {}
  }
};

console.log({...obj, ...obj2});

I've expected the result like this

{
  "a": {
    "aa": {}
  },
  "b": {},
  "c": {
    "ca": {},
    "cb": {},
    "cc": {},
    "cd": {}
  }
}

How can I achieve my expected thing?