jq - Copy values of first array element if other values are null - json

Question

I have an object which contains an array of objects. I want to replace null values of a specific key value pair with the value of the 0th array index. In the example below I want for array elements 1 to contain "website" and "email" of the "email" and "website" of the 0th array element because they are both null. For element 2 I only expect the "website" to be set with the result of the 0th array element as only that is null.
The json that I have is
{
"id": 123,
"offices": [
{
"officeId": 12345,
"name": "Name LLP",
"website": "www.example.com",
"email": "website#example.com",
"officeType": "HO"
},
{
"officeId": 123456,
"name": "Name",
"website": null,
"email": null,
"officeType": "BRANCH"
},
{
"officeId": 1234567,
"name": "Name",
"website": null,
"email": "example#website.com",
"officeType": "BRANCH"
},
],
}
My expected json output would be
{
"id": 123,
"offices": [
{
"officeId": 12345,
"name": "Name LLP",
"website": "www.example.com",
"email": "website#example.com",
"officeType": "HO"
},
{
"officeId": 123456,
"name": "Name",
"website": "www.example.com",
"email": "website#example.com",
"officeType": "BRANCH"
},
{
"officeId": 1234567,
"name": "Name",
"website": "www.example.com",
"email": "example#website.com",
"officeType": "BRANCH"
},
],
}
I have attempted to solve this using map and walk but cannot seem to find the correct way to solve it

Answer 1

After fixing the errors in your JSON file so it's valid:
jq '. as $orig |
.offices |= map(.website //= $orig.offices[0].website |
.email //= $orig.offices[0].email)' input.json
{
"id": 123,
"offices": [
{
"officeId": 12345,
"name": "Name LLP",
"website": "www.example.com",
"email": "website#example.com",
"officeType": "HO"
},
{
"officeId": 123456,
"name": "Name",
"website": "www.example.com",
"email": "website#example.com",
"officeType": "BRANCH"
},
{
"officeId": 1234567,
"name": "Name",
"website": "www.example.com",
"email": "example#website.com",
"officeType": "BRANCH"
}
]
}

Answer 2

Since you have not given any details about your attempts, let me, in the spirit of "How to Solve It", suggest a strategy for doing so.
Specifically, let's formulate and solve the obvious "subproblem" which should make the solution to the original problem easy to the point of almost being trivial. The obvious "subproblem" is: given a reference object, $ref, how to update another object so that null-valued keys in the latter are taken from $ref if available?
def infer($ref):
with_entries( if .value == null then $ref[.key] else . end);
Now the original problem becomes much easier, right?