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 = "#!/usr/bin/env python3\n\nimport math\n\ndef main():\n    [K, N] = list(map(int, input().split()))\n\n    r = []\n    if K == 1:\n        r = [1] * ((N + 1) // 2)\n    elif K % 2 == 0:\n        r = [K // 2]\n        r += [K] * (N - 1)\n    else:\n        t = N // 2\n        x = int(math.log(N * (K - 1) + 1, K) - 1)\n        while t < ((K ** (x + 1) - 1) / (K - 1) + x) // 2:\n            x -= 1\n        x += 1\n        r = [(K + 1) // 2] * (N - x)\n        r += [0] * x\n        t = ((K ** (x + 1) - 1) / (K - 1) + x) // 2 - t\n        for i in range(x, 0, -1):\n            r[N - i] = 1\n            t -= 1\n            for j in range(K - 1):\n                if t == 0:\n                    break\n                if K ** i - 1 <= t * (K - 1):\n                    r[N - i] += 1\n                    t -= (K ** i - 1) // (K - 1)\n            if t == 0:\n                break\n\n        for i in range(len(r) - 1, -1, -1):\n            if r[i] == 0:\n                r.pop()\n            else:\n                break\n\n\n    print((' '.join(list(map(str, r)))))\n\n\ndef __starting_point():\n    main()\n\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14583