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. 
x=raw_input().split(' ')
n=int(x[0])
k=int(x[1])

arr=[]
has=[0]*100001
i=1
j=1+k
l=0
while l<n and i<j:
    has[i]=1
    has[j]=1
    arr.append(i)
    arr.append(j)
    i=i+1
    j=j-1
    l=l+2
i=1
while l<n:
    while has[i]==1:
        i=i+1
    has[i]=1
    arr.append(i)
    l=l+1
i=0
while i<n:
    print arr[i],
    i=i+1
