AVL
AVL trees, developed by Russian scientists Adelson-Velsky and Landis, are a type of balanced binary search tree. In AVL terminology, a binary tree is considered balanced if, for every node, the height difference between its left and right subtrees is no more than one. Such a tree is known as an AVL tree. It is evident that there isn't a single unique AVL tree for a given number of nodes. For instance, there are six different AVL trees with five nodes, as illustrated in the figure below.
Trees with the same number of nodes can vary in height; for example, the figure below shows two trees with seven nodes, which can have heights of 2 and 3, respectively.
You are given two numbers, N and H, and your task is to determine the number of AVL trees that have N nodes and a height of H. Since this number can be quite large, provide the result modulo 786433.
Input
The input consists of a single line containing two numbers, N and H (1 ≤ N ≤ 65535, 0 ≤ H ≤ 15).
Output
Output a single number, which is the count of AVL trees with N nodes and a height of H, modulo 786433.