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, math\nimport io, os\n#data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline\nfrom bisect import bisect_left as bl, bisect_right as br, insort\nfrom heapq import heapify, heappush, heappop\nfrom collections import defaultdict as dd, deque, Counter\nfrom itertools import permutations,combinations\ndef data(): return sys.stdin.readline().strip()\ndef mdata(): return list(map(int, data().split()))\ndef outl(var) : sys.stdout.write(' '.join(map(str, var))+'\\n')\ndef out(var) : sys.stdout.write(str(var)+'\\n')\n#from decimal import Decimal\n#from fractions import Fraction\nsys.setrecursionlimit(100000)\nINF = float('inf')\nmod = 998244353\n\n\nn,k=mdata()\ndp=[[0]*(n+1) for i in range(n+1)]\ndp[0][0]=1\ndp[1][1]=1\ndp1 = [0] * (2 * n + 1)\nfor i in range(2,n+1):\n    for j in range(i,0,-1):\n        dp[i][j] = (dp[i-1][j-1] + dp1[2*j])%mod\n        dp1[j] = dp[i][j]%mod\nout(dp[n][k])\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15107