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())
e = range(1,k+1)
e.sort(reverse = True)
c = 1
for i in xrange(n):
    #c+=(i)
    print c,
    if i<k:
        if i%2==0:
            c+=e[i]
        else:
            c-=e[i]
    elif i==k:
        #print
        c=1+k+1
    else:
        c+=1
    
    
