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,collections as cl,bisect as bs\nsys.setrecursionlimit(100000)\ninput = sys.stdin.readline\nmod = 10**9+7\nMax = sys.maxsize\ndef l(): #intのlist\n    return list(map(int,input().split()))\ndef m(): #複数文字\n    return map(int,input().split())\ndef onem(): #Nとかの取得\n    return int(input())\ndef s(x): #圧縮\n    a = []\n    if len(x) == 0:\n        return []\n    aa = x[0]\n    su = 1\n    for i in range(len(x)-1):\n        if aa != x[i+1]:\n            a.append([aa,su])\n            aa = x[i+1]\n            su = 1\n        else:\n            su += 1\n    a.append([aa,su])\n    return a\ndef jo(x): #listをスペースごとに分ける\n    return " ".join(map(str,x))\ndef max2(x): #他のときもどうように作成可能\n    return max(map(max,x))\ndef In(x,a): #aがリスト(sorted)\n    k = bs.bisect_left(a,x)\n    if k != len(a) and a[k] ==  x:\n        return True\n    else:\n        return False\n\ndef pow_k(x, n):\n    ans = 1\n    while n:\n        if n % 2:\n            ans *= x\n        x *= x\n        n >>= 1\n    return ans\n\n"""\ndef nibu(x,n,r):\n    ll = 0\n    rr = r\n    while True:\n        mid = (ll+rr)//2\n\n    if rr == mid:\n        return ll\n    if (ここに評価入れる):\n        rr = mid\n    else:\n        ll = mid+1\n"""\n\nmod = 998244353\nn,k = m()\n\ndp = [[0 for i in range(n+1)] for j in range(n+1)]\n\ndp[0][0] = 1\nfor i in range(1,n+1):\n    for j in range(n,-1,-1):\n        if 2*j <= n:\n            dp[i][j] = dp[i-1][j-1] + dp[i][2*j]\n            dp[i][j] %= mod\n        else:\n            dp[i][j] = dp[i-1][j-1]\n            dp[i][j] %= mod\n\nprint(dp[n][k])'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14913