Giải bài trực tuyến

Given two integers n and k. Count the number of different trees such that:

       - Tree has exactly n nodes.

       - Each node has 0 or 2 chlidren.

       - Tree's height is exactly k.

Note:

       - An empty tree is same as an empty tree

       - tree X is same as tree Y if and only if the left subtree of X is same as the left subtree of Y and the right subtree of X is same as the right subtree of Y.

Input

Two integers n and k, inclusive.

Output

The number of trees in modulo 9901.

Example

Input:
5 3

Output:
2

Constraint

0