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 = 'import sys\nreadline = sys.stdin.readline\n\nINF = 10**9+7\ndef calc(n, k):\n    if k == 1:\n        return n\n    if n > 20:\n        return INF\n    return min(INF, (pow(k, n)-1)//(k-1))\n    \n\nK, N = list(map(int, readline().split()))\n\nif K%2 == 0:\n    ans = [K//2] + [K]*(N-1)\n    print((*ans))\nelse:    \n    ans = []\n    cnt = 0\n    half = True\n    for l in range(N, 0, -1):\n        clk = calc(l, K)\n        if half:\n            c = 1+K//2\n            if l%2 == 0:\n                cnt += 1\n            if clk//2 == cnt:\n                ans.append(c)\n                break\n            if clk//2 < cnt:\n                c -= 1\n                half = False\n                cnt -= clk//2 + 1\n                \n                while cnt >= clk:\n                    cnt -= clk\n                    c -= 1\n                if cnt == clk-1:\n                    ans.append(c)\n                    break\n        else:\n            c = K\n            while cnt >= clk:\n                    cnt -= clk\n                    c -= 1\n            if cnt == clk-1:\n                ans.append(c)\n                break\n        ans.append(c)\n    print((*ans))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: