Summary:

My trigger is supposed to update a custom field on the related Account called Owner_s_Last_Activity_Date__c with the CreatedDate of the Task any time a new task created on the Account is assigned to the Account owner.  The trigger works great in the positive case (i.e. the Related Account lookup is populated), but I'm getting a null pointer exception any time the related Account lookup is null.  I know I need to filter tasks with no related Account out of my trigger logic, but I just can't seem to figure out how to do it.  Any help would be greatly appreciated.  Thanks!

trigger UpdateAccountFromActivity on Task (after insert) {

  Map<ID, Account> parentAccts = new Map<ID, Account>();
  List<Id> listIds = new List<Id>();

  for (Task task : Trigger.new){
    if(task.AccountId!=null)
      listIds.add(task.AccountId);
  }
   
  parentAccts = new Map<Id, Account>([SELECT ID, Owner_s_Last_Activity__c, OwnerID, (SELECT ID, CreatedDate, OwnerId, AccountID FROM Tasks WHERE AccountID!=null ) FROM Account WHERE ID IN :listIds]);

  for (Task task: Trigger.new){
      Account myParentAcc = parentAccts.get(task.AccountId);
      if(myParentAcc.OwnerId == task.OwnerId && task.AccountID != null){
       myParentAcc.Owner_s_Last_Activity__c = task.CreatedDate;
        }     
      }  
   update parentAccts.values();
}