Puzzle time!

5 monkeys gather a pile of N peaches.  They agree to divide the peaches the following day.  Monkey A wakes up before the others, and wants some peaches, so he divides the peaches up evenly.  There's a leftover peach, so he rewards himself for his efforts.  He takes his share and leaves.  A gust of wind then combines the remaining 4 piles into 1.  Monkey B wakes up, and not knowing of A's actions, proceeds to do the same thing.  The same happens for the other 3 monkeys.  There are Q peaches after the final monkey takes his share.

Assuming no fractional peaches are involved, what is the smallest value of N, and the corresponding value of Q?  If you did this problem in a certain way, you should have an entire set of possible values of N and Q.

Obviously, this problem can be brute forced in various ways.  There is however, a quick and elegant solution.  In fact, this solution generalizes to K monkeys.  Can you find it?

>>11
Oh hey, your notation means that what you typed means something else entirely than what you meant.

The only reason it's ``obvious'' what you meant is because most people have very low expectations when it comes to /sci/'s mathematical literacy anyway. Otherwise, nobody would have assumed you'd be that ignorant of basic mathematical notation.
Wikipedia is right there if you need to look this kind of shit up. Fucking do it.