Help with Date filtering on measure

I have a table that has contract data and I need to show Contract YTD info. Here is an example:

Contract1 active dates 1/1/2018 - 12/31/2018

Contract2 active dates  4/1/2018 - 5/31/2019

Contract3 active dates  5/1/2018 - 12/31/2018

My data is setup so that contract2 would look like this:

Date...........Contract...........Amount.............Active
4/1/2018.......contract2.........500....................1
5/1/2018.......contract2.........600....................1
6/1/2018.......contract2.........900....................1
7/1/2018.......contract2.........500....................1
8/1/2018.......contract2.........500....................1
9/1/2018.......contract2.........400....................1
10/1/2018.....contract2.........500....................1
11/1/2018.....contract2.........500....................1
12/1/2018.....contract2.........200....................1
1/1/2019.......contract2.........500....................1
2/1/2019.......contract2.........900....................1
3/1/2019.......contract2.........500....................1
4/1/2019.......contract2.........200....................1
5/1/2019.......contract2.........100....................1

I have another regular daily transaction table (factSales) that is tracking Quantity.

What I need to do is figure out the DAX to get the total Quantity for only the contract YTD. Below is true YTD. I need to alter this so that the starting date will always be the first Contract Date for the respective contract. So, I'd want contract1 to start on 1/1/2018, Contract2 to start 4/1/2018, and contract3 to start 5/1/2018. I already have other filtering so it will only return Active contracts. My issue is with limiting the Quantity from Sales to stay within the contract date bounds.

YTDTotalInvoiced = CALCULATE(SUM(factSales[Quantity]),filter('Date','Date'[Date]<=today()-1 && 'Date'[Date]>=DATE(YEAR(TODAY()-1),1,1)))