How to convert a string to an integer in a JSON file using jq?

I use jq to transform a complex json object into a tinier one. My query is:

jq 'to_entries[]| {companyId: (.key), companyTitle: (.value.title), companyCode: (.value.booking_service_code)}' companies.json

Now, the (.key) is parsed as a string, yet I want companyId to be a number.

My result currently looks like this:

{"companyId": "1337","companyTitle": "Some company title","companyCode": "oxo"}

yet it should be like:

{"companyId": 1337,"companyTitle": "Some company title","companyCode": "oxo"}