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 = [1]
skip = k 
mx = 1
last = 0 

for i in xrange(n-1):
    if skip != 0 :
        if last % 2 == 0 and a[i] + skip > n :
            skip = n - a[i] 
        if last % 2 :
            a.append(a[i] - skip)
        else :
            a.append(a[i] + skip)
    else :
        if mx+1 > n :
            a.append(n)
        else :
            a.append(mx+1)
        skip = k + 1
        if not k % 2 :
            last -= 1
    skip -= 1
    mx = max(a[i+1], mx)
    last += 1
    #print i, a[i+1], skip
    
print ' '.join(map(str, a))