In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.
Let the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.

-----Constraints-----
 - 1 \leq N,K \leq 3 × 10^5
 - N and K are integers.

-----Input-----
Input is given from Standard Input in the following format:
K N

-----Output-----
Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.

-----Sample Input-----
3 2

-----Sample Output-----
2 1 

There are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).
The (12/2 = 6)-th lexicographically smallest one among them is (2,1).

```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 = "K, N = map(int, input().split())\nif K % 2 == 0:\n  print(K // 2, end = ' ')\n  for i in range(1, N):\n    if i != N - 1:\n      print(K, end = ' ')\n    else:\n      print(K)\nelse:\n  def superlist(L, n):\n    if n % 2 == 1:\n      return [L // 2 + 1] + superlist(L, n-1)\n    else:\n      Ax = [L // 2 + 1 for i in range(n)]\n      j = n - 1\n      for i in range(n // 2):\n        Ax[j] -= 1\n        if Ax[j] == 0:\n          j -= 1\n        else:\n          for m in range(j + 1, n):\n            Ax[m] = L\n          j = n - 1\n      return Ax\n  if K == 1:\n    for i in range((N - 1) // 2 + 1):\n      if i != (N - 1) // 2:\n        print(1, end = ' ')\n      else:\n        print(1)\n  else:\n    A = superlist(K, N)\n    for _ in range(N):\n      if _ != N - 1 and A[_] != 0:\n        print(A[_], end = ' ')\n      elif _ == N - 1 and A[_] != 0:\n        print(A[_])"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13301