You are asked to choose some time in the past to which you will travel. It could be a thousand years ago, a hundred years ago or last week. When you get there you will create a new timeline so that everything after that point will begin to play out as it would have with the addition of your influence. You might want to pick a time far enough in the past so that people don't recognize you. You could use your future knowledge to gain power, wealth or lost love but act fast since the stock market won't behave exactly the same way it did the first time around since you the butterfly will be emanating hurricanes of change from your minutest actions.
Strapped in, the machine turned on.
To the past of their choosing?
No way to know for certain.
Their new timelines would have no effect on ours.