java mongoDB 二级数组嵌套查询

场景：

会员集合下有多个会员文档，会员文档下有多个订单文档，订单买了多个商品文档

member->orders>orderItems

要求：

通过会员id和商品id验证会员是否购买过该商品。

数据示例

{
    "_id" : ObjectId("57e395c7a8a9b40d62008704"),
    "orders" : [
        {
            "_id" : ObjectId("582d5633c8ddd70b75a7a050"),
            "paid" : true,
            "status" : "PAID",
            "orderItems" : [
                {
                    "ID" : ObjectId("582d5633c8ddd70b75a7a051"),
                    "requestId" : "582d5633c8ddd70b75a7a04f",
                    "price" : "4",
                    "ultimatePrice" : "4",
                    "quantity" : NumberInt("1")
                }
            ]
        }
    ]
}

　　mongodb语句：

db.getCollection("f.member").find({_id:ObjectId("memberId……"),"orders.paid":true,"orders":{"$elemMatch":{"orderItems":{"$elemMatch" :{"ID":ObjectId("itemId……")}}}}},{"orders.$.orderItems":1})

　　java代码：

BasicDBObject itemIdDbObject=new BasicDBObject("ID",itemId);
        BasicDBObject itemsIdElem=new BasicDBObject().append(QueryOperators.ELEM_MATCH,itemIdDbObject);
        BasicDBObject orderItemsElem=new BasicDBObject().append("orderItems",itemsIdElem);
        BasicDBObject orderElem=new BasicDBObject().append(QueryOperators.ELEM_MATCH,orderItemsElem);
        BasicDBObject fiedValue=new BasicDBObject();
        fiedValue.put("_id",memberId);
        fiedValue.put("orders.paid",true);
        fiedValue.append("orders",orderElem);
        BasicDBObject retrievedFields=new BasicDBObject("orders.$",1);
        System.out.println(fiedValue.toJson());
        DBCursor rs = this.getCollection().find(fiedValue);
        DBObject explain = rs.explain();
        int count = rs.count();