Write a Python function treasure_hunt that takes as arguments positive integers mm, nn and pp and returns the number of valid configurations of the mnmn grid world that follows the following rules.

The "world" has mm columns and nn rows in it.

There is one knight, one treasure chest and p0p0 dragon(s) in the grid-world.

Dragons cannot share a square with anything else.

The knight can share a square with anything.

Dragons are indistinguishable from one another.

The inputs mm and nn will satisfy 1m,n501m,n50, and pp will be a nonnegative integer less than mn1mn1. You may assume the code will never be run where there are no valid configurations at all.