Find and update nested array

Question

My JSON object as shown below and I want to update one product details of user 1 by using User id and product id

{
   "_id": {
   "$oid": "5b544ee53379672e184c9aa2"
},
"user_firstname": "user 1",
"user_lastname": "test123",
"products": [
   {
     "_id": {
     "$oid": "5b5615741026382bf0b784a6"
    },
     "product_name": "product 1",
     "product_price": {
     "$numberInt": "25"
     },
   },
   {
     "_id": {
     "$oid": "5b5615ba1026382bf0b784a7"
    },
    "product_name": "product 2",
    "product_price": {
    "$numberInt": "25"
    },
   },
 ]
 }{
    "_id": {
      "$oid": "5b574e38b714e420683ae839"
     },
    "user_firstname": "user2",
   "user_lastname": "user last name",
   "products": [
     {
        "_id": {
        "$oid": "5b574e7fb714e420683ae83b"
     },
      "product_name": "product1",
      "product_price": {
      "$numberInt": "10"
     },
   },
   ],
  }

Here two users are there and they have some products. Now I want to update one product details of particular user by finding his ID. In the above example I want to update "$oid": "5b5615ba1026382bf0b784a7" product details of the user with id "$oid": "5b544ee53379672e184c9aa2"

This details I will get from the user

updateproducts =   {
           product_id : "5b5615ba1026382bf0b784a7"
           product_name : "updated product"
           product_price :"250"
           userID : "5b544ee53379672e184c9aa2"
        }

And this is my function

  module.exports.updateProducts = function(updateproducts, callback) {
     var id = updateproducts.product_id;
     sellers.update({ "_id": ObjectId(id) }, { '$set': updateproducts }, 
callback);
  }