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Contest: Task: Related: TaskC TaskE

Score : $600$ points

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