mongodb move documents from one collection to another collection

How can documents be moved from one collection to another collection in MongoDB?? For example: I have lot of documents in collection A and I want to move all 1 month older documents to collection B (these 1 month older documents should not be in collection A).

Using aggregation we can do copy. But what I am trying to do is moving of documents. What method can be used to move documents?

Update 2

Please do NOT upvote this answer any more. As written @jasongarber's answer is better in every aspect.

Update

This answer by @jasongarber is a safer approach and should be used instead of mine.

Provided I got you right and you want to move all documents older than 1 month, and you use mongoDB 2.6, there is no reason not to use bulk operations, which are the most efficient way of doing multiple operations I am aware of:

> var bulkInsert = db.target.initializeUnorderedBulkOp()
> var bulkRemove = db.source.initializeUnorderedBulkOp()
> var date = new Date()
> date.setMonth(date.getMonth() -1)
> db.source.find({"yourDateField":{$lt: date}}).forEach(
    function(doc){
      bulkInsert.insert(doc);
      bulkRemove.find({_id:doc._id}).removeOne();
    }
  )
> bulkInsert.execute()
> bulkRemove.execute()

This should be pretty fast and it has the advantage that in case something goes wrong during the bulk insert, the original data still exists.

Edit

In order to prevent too much memory to be utilized, you can execute the bulk operation on every x docs processed:

> var bulkInsert = db.target.initializeUnorderedBulkOp()
> var bulkRemove = db.source.initializeUnorderedBulkOp()
> var x = 10000
> var counter = 0
> var date = new Date()
> date.setMonth(date.getMonth() -1)
> db.source.find({"yourDateField":{$lt: date}}).forEach(
    function(doc){
      bulkInsert.insert(doc);
      bulkRemove.find({_id:doc._id}).removeOne();
      counter ++
      if( counter % x == 0){
        bulkInsert.execute()
        bulkRemove.execute()
        bulkInsert = db.target.initializeUnorderedBulkOp()
        bulkRemove = db.source.initializeUnorderedBulkOp()
      }
    }
  )
> bulkInsert.execute()
> bulkRemove.execute()