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. 
import sys
import math

MAXNUM = math.inf
MINNUM = -1 * math.inf
ASCIILOWER = 97
ASCIIUPPER = 65


def getInt():
    return int(sys.stdin.readline().rstrip())


def getInts():
    return map(int, sys.stdin.readline().rstrip().split(" "))


def getString():
    return sys.stdin.readline().rstrip()


def printOutput(lst):
    for ele in lst:
        sys.stdout.write(str(ele) + " ")
    sys.stdout.write("\n")


def solve(n, k):
    # n total 3 distinct
    lst = [1]

    top = n
    bottom = 2
    counter = 0

    while k - 1 > 0:
        if counter % 2 == 0:
            lst.append(top)
            top -= 1
        else:
            lst.append(bottom)
            bottom += 1
        counter += 1
        k -= 1

    if counter % 2 == 0:  # previously a bottom was added
        for i in range(bottom, top + 1):
            lst.append(i)
    else:
        for i in range(top, bottom - 1, -1):
            lst.append(i)

    return lst


def readinput():
    n, k = getInts()
    printOutput(solve(n, k))


readinput()
