Description

How many distinct structures are there for an unlabeled full binary tree (each node has either $0$ or $2$ children) with $n$ nodes and depth $k$? The depth of the root is defined as $1$.

Output the answer modulo $9901$.

Input Format

Two space-separated integers $n, k$.

Output Format

Output a single integer on one line representing the answer.

5 3

2

Hint

Constraints
For $100\%$ of the testdata, $3 \le n < 200$, $2 \le k < 100$.

USACO 2.3.

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