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 = "# -*- coding: utf-8 -*-\n\nimport sys\nsys.setrecursionlimit(10**6)\n# readline = sys.stdin.buffer.readline\nreadline = sys.stdin.readline\n\nINF = 1 << 60\n\n\ndef read_int():\n    return int(readline())\n\n\ndef read_int_n():\n    return list(map(int, readline().split()))\n\n\ndef read_float():\n    return float(readline())\n\n\ndef read_float_n():\n    return list(map(float, readline().split()))\n\n\ndef read_str():\n    return readline().strip()\n\n\ndef read_str_n():\n    return readline().strip().split()\n\n\ndef ep(*args):\n    print(*args, file=sys.stderr)\n\n\ndef mt(f):\n    import time\n\n    def wrap(*args, **kwargs):\n        s = time.perf_counter()\n        ret = f(*args, **kwargs)\n        e = time.perf_counter()\n\n        ep(e - s, 'sec')\n        return ret\n\n    return wrap\n\n\ndef gen_2d(n, m, fill=0):\n    return [[fill] * m for _ in range(n)]\n\n\n@mt\ndef slv(N, K):\n    memo = gen_2d(N+1, 2*N+1)\n    memo[0][0] = 1\n    M = 998244353\n    for n in range(1, N+1):\n        for k in range(n, 0, -1):\n            x = memo[n-1][k-1]\n            x += memo[n][k*2]\n            x %= M\n            memo[n][k] = x\n    return memo[N][K]\n\n\ndef main():\n    N, K = read_int_n()\n    print(slv(N, K))\n\n\ndef __starting_point():\n    main()\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15841