Determining whether a Mongo document is the first one with a particular attribute - mongodb

Question

I need to produce a report on a set of documents with timestamps between two dates. The report needs to list each document, but it also needs to include a field for each document to indicate whether it's the first document in its group, which is indicated by an attribute.
There's a slight complication in the fact that although only documents between the two dates should be included, documents before the start date need to be considered when deciding if each document is the first it its set.
E.g. given the data
{ "_id": 1, "group": "A", "timestamp": "2015-01-01" }
{ "_id": 2, "group": "B", "timestamp": "2015-01-02" }
{ "_id": 3, "group": "A", "timestamp": "2015-01-03" }
{ "_id": 4, "group": "C", "timestamp": "2015-01-04" }
{ "_id": 5, "group": "B", "timestamp": "2015-01-05" }
{ "_id": 6, "group": "C", "timestamp": "2015-01-06" }
Generating a report from 2015-01-02 to 2015-01-05 would return
{ "_id": 2, "group": "B", "timestamp": "2015-01-02", "first": 1 }
{ "_id": 3, "group": "A", "timestamp": "2015-01-03", "first": 0 }
{ "_id": 4, "group": "C", "timestamp": "2015-01-04", "first": 1 }
{ "_id": 5, "group": "B", "timestamp": "2015-01-05", "first": 0 }
Currently I'm doing this by sorting all documents by group then timestamp, then looping over the entire dataset keeping track of the previous row to decide if a row inside the date range is the first of its type. With a large dataset this is very slow - it feels as though there must be a better way involving grouping or something clever but my Mongo skills aren't up to the job - any suggestions?