Permutation p is an ordered set of integers p_1,   p_2,   ...,   p_{n}, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p_1,   p_2,   ...,   p_{n}.

Your task is to find such permutation p of length n, that the group of numbers |p_1 - p_2|, |p_2 - p_3|, ..., |p_{n} - 1 - p_{n}| has exactly k distinct elements.


-----Input-----

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 10^5).


-----Output-----

Print n integers forming the permutation. If there are multiple answers, print any of them.


-----Examples-----
Input
3 2

Output
1 3 2

Input
3 1

Output
1 2 3

Input
5 2

Output
1 3 2 4 5



-----Note-----

By |x| we denote the absolute value of number x.

```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\n\ndef solve():\n    r = list(map(int, input().split()))\n    n = r[0]\n    k = r[1]\n    l = list()\n    l.append(1)\n    c = k\n    justI = 0\n    maxsofar = 1\n    for i in range(1,n):\n        if justI == 1:\n            l.append(maxsofar+1)\n            maxsofar+=1\n        else:\n            l.append(l[i-1]+c)\n            maxsofar = max(maxsofar, l[i-1]+c)\n            if c>1:\n                c-=1\n                c*=-1\n            elif c<-1:\n                c+=1\n                c*=-1\n            else:\n                justI = 1\n    return l\n    \ndef read(mode=2):\n    inputs = input().strip()\n    if mode == 0: return inputs  # String\n    if mode == 1: return inputs.split()  # List of strings\n    if mode == 2: return list(map(int, inputs.split()))  # List of integers\ndef write(s="\\n"):\n    if s is None: s = ""\n    if isinstance(s, list): s = " ".join(map(str, s))\n    if isinstance(s, tuple): s = " ".join(map(str, s))\n    s = str(s)\n    print(s, end="")\ndef run():\n    if sys.hexversion == 50594544 : sys.stdin = open("test.txt")\n    res = solve()\n    write(res)\nrun()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14477