Counting Full Binary Trees

Count how many different binary trees satisfy all of the following conditions.

1. The tree has exactly n nodes. (1 <= n < 200)
2. Every node has degree 0 or 2. The degree of a node is the number of children it has.
3. The height of the tree is exactly k. (1 < k < 100) The height is the number of nodes on the longest path from the root to a leaf. A leaf is a node with no children.

Because the tree is binary, changing the placement of left and right children can make a different tree.

The answer can be very large, so compute it modulo 9901.

The first line contains two integers n and k.

Output the number of different binary trees satisfying the conditions, modulo 9901.