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. 
from fractions import gcd

[n,k] = [int(s) for s in input().split()]

sign = 1
p = [0 for i in range(n)]
kk = k
p[0] = 1
i = 0
while kk>0:
    p[i+1] = p[i]+sign*kk
    i = i+1
    sign = -sign
    kk = kk-1
i = i+1
if i<n:
    p[i] = k+2
while i<n-1:
    p[i+1] = p[i]+1
    i = i+1
print(' '.join(map(str,p)))
##while 1>0:
##    line = input()
##    if len(line.split())==0:
##        break
##    print(line)
