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())
if k == 1:
    for i in range(1,n+1):
        print i,
else:
    print 1,
    f,s=2,n 
    ok = True
    while k > 1:
        if ok:
            print s,
            s-=1
            ok=False
        else:
            print f,
            f+=1
            ok=True
        k-=1
    if ok:
        for i in range(f,s+1):
            print i,
    else:
        for i in range(s,f-1,-1):
            print i,
        