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. 
n,k=map(int,raw_input().split())
a=[]
if k==1:
    for i in range(1,n+1):
        print i,
elif k==2:
    print 1,3,2,
    for i in range(4,n+1):
        print i,
else:
    a=[]
    cnt1=1
    cnt2=n
    x=k%2
    k=k/2
    if x==0:
        k=k-1
    i=0
    while i<k:
        a.append(cnt1)
        a.append(cnt2)
        i+=1
        cnt1+=1
        cnt2-=1
    i+=1
    cnt2+=1
    while i<cnt2:
        a.append(i)
        i+=1
    if x==0:
        t=a[n-2]
        a[n-2]=a[n-1]
        a[n-1]=t
    for i in range(n):
        print a[i],
    
