201073: [AtCoder]ARC107 D - Number of Multisets

Problem Statement

You are given two positive integers $N$ and $K$. How many multisets of rational numbers satisfy all of the following conditions?

• The multiset has exactly $N$ elements and the sum of them is equal to $K$.
• Each element of the multiset is one of $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$. In other words, each element can be represented as $\frac{1}{2^i}\ (i = 0,1,\dots)$.

The answer may be large, so print it modulo $998244353$.

Constraints

• $1 \leq K \leq N \leq 3000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the number of multisets of rational numbers that satisfy all of the given conditions modulo $998244353$.

Sample Input 1

4 2

Sample Output 1

2

The following two multisets satisfy all of the given conditions:

• ${1, \frac{1}{2}, \frac{1}{4}, \frac{1}{4}}$
• ${\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}}$

Sample Input 2

2525 425

Sample Output 2

687232272