return name of the array that contains certain key with jq

I have the following JSON:

{
  "somekey": "somevalue",
  "blue_services": [
    "service-a",
    "service-b",
    "service-c"
  ],
  "otherkey": "othervalue",
  "red_services": [
    "service-d",
    "service-e",
    "service-f"
  ],
  "black_services": [
    "service-g",
    "service-h",
    "service-i"
  ]
}

I want jq to return the name of the array that contains certain value:

for example:

if I look for service-a jq should return blue_services
if I look for service-h jq should return black_services

I manage to extract the arrays that match certain regexp with:

keys[] | select(test ("[aA-zZ]_services"))

But i dont know how to then search inside for a match and return the relevant name, I have also tried piping to contains/has/any

ideally I would like to use a variable to be able to do several searches for service-x

>Solution :

You could use to_entries to get an array of key-value pairs. Search the values using IN, and output the key. Use --arg to import a string from the command-line.

jq -r --arg q "service-a" 'to_entries[] | select(IN($q; .value[]?)).key'

blue_services

Demo