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 = "# region header\nimport sys, bisect, math, itertools, heapq, collections\nfrom operator import itemgetter\n# a.sort(key=itemgetter(i)) # i番目要素でsort\nfrom functools import lru_cache\nimport copy\n# @lru_cache(maxsize=None)\n# sys.setrecursionlimit(10**8)\ninput = sys.stdin.readline\nINF = float('inf')\nmod = 10**9 + 7\neps = 10**-7\n# endregion\n# region input function\n\n\ndef inp():\n    '''\n    一つの整数\n    '''\n    return int(input())\n\n\ndef inpl():\n    '''\n    一行に複数の整数\n    '''\n    return list(map(int, input().split()))\n\n\ndef str_inp():\n    '''\n    文字列をリストとして読み込む\n    '''\n    return list(input()[:-1])\n\n\n# endregion\nmod = 998244353\nn, k = inpl()\ndp = [[0] * (n + 1) for _ in range(n + 1)]\n# i個使ってjを作れる個数\nfor i in range(1, n + 1):\n    for j in range(1, i + 1)[::-1]:\n        if i == j:\n            dp[i][j] = 1\n            continue\n        # 1を使う(i-1個使ってj-1を作ったものに1を添える)\n        a = dp[i - 1][j - 1]\n        # 1を使わない(1を含めてi個使って2jを作り、全体を1/2する)\n        b = dp[i][2 * j] if 2 * j < n + 1 else 0\n        dp[i][j] = (a + b) % mod\nprint((dp[n][k] % mod))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 177674