Need help parsing json output with jq for a complex json

Question

For the below JSON, I need the result.id and result.name output using jq for the ones having

authorization.roles[].name == "Supervisor" 

What is the command for jq to to that ? For the below json we expect 1231 id and name AAAA alone as output as that only has Supervisor as role

{
    "results": [{
        "id": "1231",
        "name": "AAAA",
        "div": {
            "id": "AAA",
            "name": "DDSAA",
            "selfUri": ""
        },
        "chat": {
            "jabberId": "nn"
        },
        "department": "Shared Services Organization",
        "email": "[email protected]",
        "primaryContactInfo": [{
            "address": "[email protected]",
            "mediaType": "EMAIL",
            "type": "PRIMARY"
        }],
        "addresses": [],
        "state": "active",
        "title": "AAA",
        "username": "[email protected]",
        "version": 27,
        "authorization": {
            "roles": [{
                "id": "01256689-c5ed-43a5-b370-58522402830d",
                "name": "AA"
            }, {
                "id": "1e65b009-9f8f-4eef-9844-83944002c095",
                "name": "BBB"
            }, {
                "id": "8a19f1ff-40e5-45d2-b758-14550a173323",
                "name": "CCC"
            }, {
                "id": "d02250e2-7071-46bf-885b-43edff2d88a6",
                "name": "Supervisor"
            }]
        }
    }, {
        "id": "1255",
        "name": "BBBB",
        "div": {
            "id": "AAA",
            "name": "DDSAA",
            "selfUri": ""
        },
        "chat": {
            "jabberId": "nn"
        },
        "department": "Shared Services Organization",
        "email": "[email protected]",
        "primaryContactInfo": [{
            "address": "[email protected]",
            "mediaType": "EMAIL",
            "type": "PRIMARY"
        }],
        "addresses": [],
        "state": "active",
        "title": "AAA",
        "username": "[email protected]",
        "version": 27,
        "authorization": {
            "roles": [{
                "id": "01256689-c5ed-43a5-b370-58522402830d",
                "name": "AA"
            }, {
                "id": "1e65b009-9f8f-4eef-9844-83944002c095",
                "name": "BBB"
            }, {
                "id": "8a19f1ff-40e5-45d2-b758-14550a173323",
                "name": "CCC"
            }, {
                "id": "d02250e2-7071-46bf-885b-43edff2d88a6",
                "name": "Tester"
            }]
        }
    }]
}