Hoe te filteren op maand- en jaarbereik in Mongodb

Ik heb het zelf:

db.bills.aggregate([
{
    $match: {
        $expr: {
            $or: [
                {
                    $and: [
                        {$eq: ["$year", FROMYEAR]},
                        {$eq: ["$year", TOYEAR]},
                        {$gte: ["$month", FROMMONTH},
                        {$lte: ["$month", TOMONTH},
                    ]
                },
                {
                    $and: [
                        {$eq: ["$year", FROMYEAR]},
                        {$lt: ["$year", TOYEAR]},
                        {$gte: ["$month", FROMMONTH]}
                    ]
                },
                {
                    $and: [
                        {$gt: ["$year", FROMYEAR]},
                        {$eq: ["$year", TOYEAR]},
                        {$lte: ["$month", TOMONTH]}
                    ]
                },
                {
                    $and: [
                        {$gt: ["$year", FROMYEAR]},
                        {$lt: ["$year", TOYEAR]}
                    ]
                }
            ]
        }
    }
},
{
    $project: {
        "id": 1,
        "month": 1,
        "year": 1,
        "_id": 0
    }
},
,
{
    $sort: {
        "year": 1,
        "month": 1
    }
}
]).toArray()

De eerste is om fromYear, fromMonth, toYear, toMonth uit de query te extraheren. De volgende is om het in te stellen op de overeenkomstige positie in de zoekopdracht. Er zijn 4 bereiken die overeenkomen:

MinYear = $year = MaxYear ==========> MinMonth < $month < MaxMonth
MinYear = $year < MaxYear ==========> MinMonth <= $month
MinYear < $year = MaxYear ==========> $month <= MaxMonth
MinYear < $year < MaxYear ==========> any $month

Het resultaat ziet er als volgt uit:

[
    {
        "id" : "BI_0010",
        "month" : 5,
        "year" : 2017
    },
    {
        "id" : "BI_0008",
        "month" : 3,
        "year" : 2018
    },
    {
        "id" : "BI_0001",
        "month" : 8,
        "year" : 2018
    }
]