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. 
#!/usr/bin/python

from collections import deque

def ia():
    line = raw_input()
    line = line.split()
    return map(int, line)

n, k = ia()


def pd(a):
    s = set()
    for i in range(n):
        if i+1<n:
            d = abs(a[i] - a[i+1])
            s.add(d)
    print list(s)


def make_init():
    a = [None] * n
    j = 1
    k = n
    for i in range(0, n, 2):
        if i+1<n: a[i+1] = k
        a[i] = j
        j = j + 1
        k = k - 1
    return a


a = make_init()

if a[k-1]>n//2:
    p = a[k-1]-1
    for i in range(k, n):
        a[i] = p
        p = p - 1
else:
    p = a[k-1]+1
    for i in range(k, n):
        a[i] = p
        p = p + 1

print ' '.join(map(str, a))
