In the TV game show Gladiators, the final competition is to run through a steeplechase course. To get some variation, the producer has decided to change the course each week. The course is always built out of m obstacles, all of different heights, placed along a straight line. An obstacle consists of two initially connected platforms which may be separated. Between the two platforms of an obstacle, other higher obstacles may be put. Also, obstacles may be put after one another.
The producer thinks it is most desirable that the results from different weeks may be compared to each other. Therefore, he wants to build courses of similar degree of difficulty.
A proposed measure of difficulty is the number of platforms that are higher than their immediately preceeding platform along the course. Moreover, the leftmost (first) platform of the course always give rise to one point since it is located above the floor. E.g. the course to the right in figure 1 has four points of difficulty.
Your mission is to find out how many ways there are to build a course of a given point of difficulty,from a given number of obstacles.