can see okay for all values of K of X capital T which one is the most likely if it gets to be completed in its optimal way you pick that one followed from that value to what the previous values should be previous value all the way back to the front so very efficient algorithm and you can do this for example in a tabular case you can do it in general as long as the competition is tractable as long as you can do that maximization sometimes a maximization is easier to do that an integral so sometimes this thing is more tractable