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-----
4 2

-----Sample Output-----
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}}

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ntry:\n    import os\n    f = open(\'input.txt\', \'r\')\n    sys.stdin = f\nexcept FileNotFoundError:\n    None\nfrom math import sqrt, ceil, floor\nfrom collections import deque, Counter, defaultdict\n# defaultdict(int)\ninput=lambda: sys.stdin.readline().strip()\nsys.setrecursionlimit(11451419)\nfrom decimal import ROUND_HALF_UP,Decimal  #変換後の末尾桁を0や0.01で指定\n  #Decimal((str(0.5)).quantize(Decimal(\'0\'), rounding=ROUND_HALF_UP))\nfrom functools import lru_cache\nfrom bisect import bisect_left as bileft, bisect_right as biright, insort\nfrom itertools import combinations as com, permutations as per\nfrom fractions import Fraction as frac  #frac(a,b)で正確なa/b\n# @lru_cache(maxsize=10**10)\n#######ここまでテンプレ#######\n#ソート、"a"+"b"、再帰ならPython3の方がいい\n#######ここから天ぷら########\n\nn,k=list(map(int,input().split()))\nmod=998244353\n# @lru_cache(maxsize=10**10)\n# def saiki(n,k):\n#     print(n,k,flush=1)\n#     if n<k:return 0\n#     if n==k:return 1\n#     if n==0:return 0\n#     if k==0: return 0\n#     if n==1:return 1\n#     if k==1: return saiki(n,2*k)\n#     return (saiki(n-1,k-1)+ saiki(n,2*k))%mod\n\ndp=[[0]*3002 for  i in range(3003)]\n# dp[1][1]=1\nfor i in range(1,n+1):\n    for j in range(n,0,-1):\n        if i<j:dp[i][j]=0\n        elif i==j : dp[i][j]=1\n        elif 2*j >i: dp[i][j]=dp[i-1][j-1]\n        else: dp[i][j]=(dp[i-1][j-1]+ dp[i][2*j])%mod\n\nprint((dp[n][k]))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 72320941