Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

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. 
# -*- coding: utf-8 -*-
import math
import sys
from collections import defaultdict
import collections
import heapq


class Solver(object):

    def run(self):
        n, k = readarray(int)

        res = []
        res.append(1)
        num = 1
        for i in xrange(k, 0, -1):
            if i % 2 == k % 2:
                num += i
            else:
                num -= i
            res.append(num)

        for i in xrange(1 + k + 1, n+1):
            res.append(i)

        print(" ".join(map(str, res)))




################################################################################
# ここからは見ちゃダメ！

def read(foo):
    return foo(raw_input())
def readarray(foo):
    return [foo(x) for x in raw_input().split()]
def dbg(a):
    sys.stderr.write(str(a))
def dbgln(a):
    sys.stderr.write(str(a) + "\n")

if __name__ == '__main__':
    Solver().run()
