How to write mongoDB query to sum up elements in an array that match another array?

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database

MongoDB

schema

NoSQL

In my mongoDB dbs there is a collection A1 that has an array of embedded objects B. I want to group all elements in A1 by the sum of a certain field of B in the array field of A1,namely X. Meanwhile the value of X field need to be an element in another collection A2. That's to say I need to sum up the elements in B array with the X field matching the elements in A2 collection for grouping A1 rather than sum up all elements in B array. I have wrote a query but don't know if it's correct. If not, how to modify it to the right one?

db.A1.aggregate([{$match:{B.X: {$in:A2}}},
                 {$group:{_id:"$ID",Sum: { $sum:"$B.X"}}},
                 {$sort:{Sum: 1}}
                ])