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 bisect, collections, copy, heapq, itertools, math, string\nimport sys\ndef I(): return int(sys.stdin.readline().rstrip())\ndef MI(): return list(map(int, sys.stdin.readline().rstrip().split()))\ndef LI(): return list(map(int, sys.stdin.readline().rstrip().split()))\ndef S(): return sys.stdin.readline().rstrip()\ndef LS(): return list(sys.stdin.readline().rstrip().split())\nfrom collections import deque, defaultdict, Counter\nimport heapq\nfrom functools import reduce\nfrom itertools import permutations\nimport math\nimport bisect\n\ndef main():\n    mod = 998244353\n    def comp(x, y):\n        if x < y:\n            return 0\n        return dp[x][y]\n    N, K = MI()\n    dp = [[0 for _ in range(N + 1)]for _ in range(N + 1)]\n    dp[0][0] = 1\n    dp[0][1] = 0\n    dp[1][0] = 0\n    dp[1][1] = 1\n    for i in range(2, N + 1):\n        for j in range(N, 0, -1):\n            dp[i][j] = comp(i - 1, j - 1) + comp(i, 2 * j)\n            dp[i][j] %= mod\n    #print(dp)\n    print((dp[N][K]))\ndef __starting_point():\n    main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 178639