Group sum and transform json object with values in nested array

I am trying to aggregate and transform the following json :

[
{ 
    "orderId" : "01",
    "date" : "2017-01-02T06:00:00.000Z",
    "items" : [
        {
            "itemId": 100,
            "itemCost": 12,
            "itemQuantity": 10
        },
        {
            "itemId": 102,
            "itemCost": 25,
            "itemQuantity": 4
        }
    ]
},
{
    "orderId": "02",
    "date" : "2017-01-08T06:00:00.000Z",
    "items" : [
        {
            "itemId": 100,
            "itemCost": 15,
            "itemQuantity": 2
        },
        {
            "itemId": 101,
            "itemCost": 20,
            "itemQuantity": 5
        },
        {
            "itemId": 102,
            "itemCost": 25,
            "itemQuantity": 1
        }
    ]
},
{
    "orderId": "03",
    "date" : "2017-02-08T06:00:00.000Z",
    "items" : [
        {
            "itemId": 100,
            "itemCost": 15,
            "itemQuantity": 2
        },
        {
            "itemId": 101,
            "itemCost": 20,
            "itemQuantity": 5
        },
        {
            "itemId": 102,
            "itemCost": 25,
            "itemQuantity": 1
        }
    ]
}]

into an object that is grouped by itemId, and then aggregated by quantity, and aggregated by total cost (item cost * item quantity for each order) by month. Example:

[
    {
        "itemId": 100,
        "period": [
            {
                "month": "01/17",
                "quantity": 12,
                "cost": 130
            }
        ]
    },
    {
        "itemId": 101,
        "period": [
            {
                "month": "01/17",
                "quantity": 5,
                "cost": 100
            },
            {
                "month": "02/17",
                "quantity": 5,
                "cost": 100
            }
        ]
    },
    {
        "itemId": 102,
        "period": [
            {
                "month": "01/17",
                "quantity": 5,
                "cost": 125
            },
            {
                "month": "02/17",
                "quantity": 1,
                "cost": 25
            }
        ]
    }
]

I have a small indention on my desk in which I have been beating my head trying to figure how to do this using native map/reduce or lodash.